A Consumer Surplus Can Be Best Described as:

Consumer Surplus

Consumer surplus is defined as the area beneath the demand curve and above the market-clearing price from the origin to the market-clearing quantity of consumption for the adept in question.

From: Encyclopedia of Biodiversity (Second Edition) , 2013

Consumer Welfare

David K. Mandy , in Producers, Consumers, and Fractional Equilibrium, 2017

12.v Exercises

1.

Advisedly graph the EV and CV for a price subtract of a normal good. Place the Marshallian demands after both variations on your graph. Illustrate the deadweight losses based on both the EV and CV.

2.

Advisedly graph the EV and CV for a price increase of an inferior good. Identify the Marshallian demands after both variations on your graph. Illustrate the deadweight losses based on both the EV and CV.

iii.

A consumer has expenditure part $e^{*}=\sqrt{p_1}$ for some particular level of utility. The price p ₁ increases from 1 to 100. What is the compensating variation of this cost modify? Why?

iv.

Using ϕ from Exercise 7a of Affiliate ix, what is the compensating variation of an increase in p ₁ from $p_1^0$ to $p_1^{\mathrm{ane}}$ , for given m and p ₂?

5.

A consumer has continuous, complete, and transitive preferences on ${\mathbb{R}}_{+}^2$ with indifference curves that appear equally follows:

Graph and depict the deadweight loss caused by an increment in the price of ten ₁.

vi.

Here is a utility function on ${\mathbb{R}}_{+}^2$ : u(10 ₁, x ₂) = 10 _ane ten ₂ + ten ₁. Let p _i announce the price of commodity i and m denote money income. Presume p ₁ = 1 and m = 50. Notice the deadweight loss in consumer welfare due to an increase in p ₂ from ${\widehat{p}}_{\mathrm{ii}}=2$ to ${\tilde{p}}_{\mathrm{two}}=4$ .

seven.

Suppose the Hicksian demand ${ĥ}^{\perp }=ū\left(\frac{p_2}{p_{\mathrm{i}}},\frac{p_1}{p_2}\right)$ has been econometrically estimated. Based on this approximate, what is the equivalent variation of a change in p _one from p ₁ = 1 to p _ane = 31 when income is m = 160 and p ₂ = 1?

8.

A consumer has Hicksian demand ${ĥ}^{\perp }={\left({\mathrm{due\; east}}^{ū}\right)}^{1/2}\left({\left(\frac{p_2}{p_1}\right)}^{1/2},{\left(\frac{p_1}{p_{\mathrm{two}}}\right)}^{1/\mathrm{ii}}\right)$ . Suppose p ₂ = i and money income is m = viii. Consider a change in p _i from $p_{\mathrm{ane}}^0=1$ to $p_1^{\mathrm{i}}=2$ . Summate the percent fault if the change in Marshallian surplus is used to measure out the welfare modify rather than the compensating variation (surplus and CV both on commodity ane).

9.

A consumer receives utility $u=\sqrt{x}+y$ from consuming quantity 10 of one good and quantity y of a second practiced (x and y both in ${\mathbb{R}}_{+}^1$ ). This consumer has income m = 10 to spend. Allow p denote the relative toll per unit of 10 (the price of y is normalized to ane).

a.

Calculate the error if we use the change in Marshallian surplus for skilful x equally a mensurate of the utility gain due to a price subtract from p = .04 to p = .03.

b.

What happens if the price change nether consideration is from p = .03 to p = .02?

10.

A consumer has the following utility function on ${\mathbb{R}}_{+}^3$ : $u=x_1{\mathrm{10}}_2{\mathrm{eastward}}^{x_3}$ . Allow thou, p _ane, and p ₂ announce money income and the prices of bolt x ₁ and 10 ₂, respectively, relative to the price of commodity x _three.

a.

Find the Marshallian need correspondence in terms of m, p _one, and p ₂. Hint: Be careful to distinguish between the ${\widehat{x}}_{\mathrm{three}}=0$ and ${\widehat{\mathrm{ten}}}_{\mathrm{iii}}>0$ cases.

b.

Notice the indirect utility function in terms of 1000, p ₁, and p ₂.

c.

Find the expenditure function in terms of $ū$ (the utility level), p ₁, and p ₂.

d.

Suppose p _ii = m = ane. Find the compensating variation of an increment in p ₁ from i to 4. Draw a graph of Marshallian and Hicksian demands that illustrates your respond.

eastward.

Now suppose m = four. How does your answer to part (d) alter? Add the need data to your graph from part (d) that conspicuously illustrates the difference between the g = i instance and the 1000 = 4 case.

eleven.

Consider a consumer of three goods in ${\mathbb{R}}_{+}^3$ with prices p ₁, p ₂, and p ₃. Allow yard denote the endowed coin income of this consumer. This consumer's indirect utility part is:

$\begin{array}{l}\hfill u^{*}(p_1,p_2,p_{\mathrm{three}},m)=\frac{m}{p_{\mathrm{ane}}+p_{\mathrm{ii}}+p_3}\end{array}$

for positive prices and non-negative incomes.

a.

Find the Marshallian need correspondence.

b.

Verify that your answer to office (a) satisfies the necessary and sufficient conditions for the Marshallian need of a consumer with locally nonsatiated preferences.

c.

Suppose 1000 = 100, p _ii = 1, and p ₃ = 2. Notice the compensating and equivalent variations for a change in p _ane from p ₁ = 1 to p _i = 7.

d.

Find a (straight) utility function for which u* is the indirect utility function.

eastward.

Are this consumer's preferences consummate, transitive, and continuous on ${\mathbb{R}}_{+}^3$ ? Why?

12.

Suppose indirect utility is:

$\begin{array}{l}\hfill u^{*}(p_{\mathrm{i}},p_2,p_{\mathrm{three}},m)=\frac{\mathrm{one\; thousand}}{p_1^{\mathrm{i}/2}{p}_2^{\mathrm{one}/4}{p}_3^{\mathrm{i}/4}}.\end{array}$

a.

Verify that the u* function satisfies the sufficient weather to exist an indirect utility function.

b.

Derive the expenditure function.

c.

Calculate the equivalent variation of a toll increment from p _iii = 16 to p ₃ = 81 when p _one = 9, p ₂ = 16, and m = 36.

d.

Derive the Hicksian need for article three. What are the (Hicksian) quantities demanded for article iii at the two cost vectors under consideration in role (c) and utility level u*(9, 16, 81, 36)?

e.

Calculate the truthful deadweight loss of the price increase in office (c) at utility u*(nine, 16, 81, 36).

f.

Derive the Marshallian need for commodity 3. What are the (Marshallian) quantities demanded for commodity iii at the two price/income vectors nether consideration in part (c)?

g.

Calculate the deadweight loss of the price increase in part (c) based on the Marshallian need for article 3 (Note: Use $ln(\mathrm{three}/2)\approx \mathrm{0.four}$ ).

h.

Compare the true deadweight loss in part (e) with the Marshallian deadweight loss in part (yard). How large is the error in the Marshallian measure equally a pct of the true deadweight loss?

i.

Verify that the Hicks-Slutsky Decomposition holds for a change in the demand for article 3 with respect to the price of article 3.

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Economics of the Regulating Services

Edward B. Barbier , in Encyclopedia of Biodiversity (Second Edition), 2013

Glossary

Consumer surplus

A measure of the welfare that people gain from the consumption of goods and services, usually measured as the difference between the price that they are actually willing and able to pay for a good or service and the actual market toll.

Direct apply values

Benefits gained through consumptive and nonconsumptive uses that involve some grade of direct physical interaction with environmental goods and services, such as recreational activities, resource harvesting, drinking clean water, breathing unpolluted air, then forth.

Economic valuation

The diverse methods used past economists to determine the willingness to pay of individuals for the benefits derived from ecosystems, many of which are nonmarketed.

Ecosystem functions

Biogeochemical cycling, including primary production (photosynthesis), nutrient and water cycling, and materials decomposition, and the flow, storage and transformation of materials, and energy through an ecosystem, including through food spider web processes such every bit pollination, predation, and parasitism.

Ecosystem services

The benefits (i.e., goods and services) people obtain from ecosystems.

Ecosystem structure

The biotic (living) and abiotic (nonliving) components of an ecosystem, and the interactions between them.

Indirect apply values

Ecosystem services or benefits whose values tin can only be measured indirectly, since they are derived from supporting and protecting activities that accept directly measurable values (eastward.m., coastal habitat equally breeding and nursery grounds for off-shore fisheries; coral reefs providing protection confronting storm surge; upper watershed forests controlling soil erosion and runoff).

Nonuse values

Values ascribed to the natural environment that are contained of whatever human interaction with it; for case, an private valuing the pure "beingness" of a natural habitat or ecosystem or wanting to "bequest" it to future generations.

Producer surplus

A mensurate of the welfare that producers proceeds from selling goods and services, usually measured equally the departure between the bodily marketplace price and the minimum amount that they would be willing to accept for the adept or service.

Regulating services

The benefits obtained from the regulation of ecosystem processes, including inundation protection, climate regulation, human affliction regulation, h2o purification, air quality maintenance, pollination, and pest command.

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Handbook of Media Economic science

Matthew Gentzkow , ... Daniel F. Stone , in Handbook of Media Economic science, 2015

14.5 Supply-Driven Bias

One potential driver of bias is that firms may adopt consumers to have particular deportment. Such preferences could arise from many sources. Chapter 16 in this handbook considers incentives arising from pressure by governments, advertisers, or other third parties. Here, we consider incentives internal to the firm. These could include direct political or business-related preferences of media owners, or arise indirectly, from the preferences of reporters or editors.

The literature has reached three principal conclusions near the implications of supply-driven bias. First, supply-side incentives can drive both filtering and baloney bias in equilibrium and can atomic number 82 to manipulation of even rational, sophisticated consumers. If persuasive incentives are stiff enough relative to the profit motive, firms volition prefer to tilt their reports to bear on consumer actions even at the cost of profits. Second, contest generally reduces distortion and moves outcomes back toward what would occur in the absenteeism of persuasive incentives, even if the competing firms have like biases. Intuitively, contest tends to align outcomes ameliorate with the demand of consumers, which in the baseline case is for unbiased news. Tertiary, competition tends to increase consumer welfare although it may increase or decrease total surplus once the ideological payoff of the owners is taken into account.

To illustrate these results in the context of our model, we assume that each firm has a preferred action. In add-on to its monetary profit, the firm earns a payoff equal to $\alpha >0$ times the fraction of consumers taking its desired action. We call firms whose preferred action is A _R correct-biased and firms whose preferred activeness is A _L left-biased.

Equally shown in a higher place, the fraction of (homogeneous, centrist) consumers who get news is $G\left(0.5\left({\sigma }_l+{\sigma }_r-1\right)\right)$ . Consumers who do not go news are indifferent between actions, so suppose they choose A _L with probability 0.5. The probability that a consumer who does become news chooses A _L is ${\sigma }_l\mathit{Pr}\left(L\right)+\left(1-{\sigma }_r\right)\mathit{Pr}\left(R\right)=\mathrm{0.v}\left({\sigma }_l+\mathrm{i}-{\sigma }_r\right)$ . Thus, the expected fraction of all consumers choosing A _L is $0.5\left({\sigma }_l+\mathrm{i}-{\sigma }_r\right)G\left(0.5\left({\sigma }_l+{\sigma }_r-1\right)\right)+0.5\left(\mathrm{ane}-\mathrm{1000}\left(0.5\left({\sigma }_l+{\sigma }_r-1\right)\right)\right)$ .

Suppose in that location is just ane left-biased firm. Then its objective function is α times the fraction of consumers choosing A _L plus ρ times the fraction of consumers consuming news:

(14.2) $\begin{array}{c}\hfill {\Pi }_M=\alpha \left[0.5\left({\sigma }_l+1-{\sigma }_r\right)\mathrm{Chiliad}\left(0.5\left({\sigma }_l+{\sigma }_r-1\right)\right)+0.5\left(\mathrm{one}-G\left(0.5\left({\sigma }_{\mathrm{50}}+{\sigma }_r-\mathrm{ane}\right)\right)\right)\right]\hfill \\ +\rho \mathrm{Grand}\left(0.5\left({\sigma }_{\mathrm{fifty}}+{\sigma }_r-\mathrm{ane}\right)\right)\hfill \\ \hfill =\alpha \left(0.5\left({\sigma }_l-{\sigma }_r\right)\mathrm{Chiliad}\left(0.5\left({\sigma }_l+{\sigma }_r-1\right)\right)+0.5\right)+\rho \mathrm{1000}\left(\mathrm{0.five}\left({\sigma }_l+{\sigma }_r-\mathrm{one}\right)\right)\hfill \end{array}.$

For distortion bias, the derivative of this expression with respect to b is negative when $b\ge 0$ for sufficiently large α and pocket-size ρ, and it is straightforward to show Π ₁₀₀₀ is non maximized when $b=-\mathrm{one}$ , and then there exists an interior optimum, $b^{*}\in \left(-\mathrm{ane},0\right)$ if α(ρ) is large (small) plenty. It tin can be shown with implicit differentiation that $\left|b^{*}\right|$ is increasing in α and decreasing in ρ. Discover that bias influences the distribution of consumer deportment in equilibrium even though consumers are rational. This is an example of rational persuasion as in Kamenica and Gentzkow (2011).

To see the effect of contest, note first that all consumers will choose whichever house has the lowest $\left|b\right|$ . If there were a 2nd firm with an opposing preference for consumer actions, then the two firms each offering biased news cannot be an equilibrium since if either firm had an equal or greater bias (than its competitor), then information technology could be strictly better off in terms of both profits and consumer actions by undercutting its competitor'south bias. The only equilibrium is both firms offering unbiased news. More surprisingly, the same result occurs when both firms take the same preference for consumer deportment. If one firm offered biased news, the other firm could obtain the entire market by undercutting this bias marginally, while but marginally decreasing the desired consumer deportment. Thus, there would always exist an incentive to undercut if either business firm offered biased news.

Since consumer welfare is decreasing in bias, clearly welfare is higher in duopoly. Results are very like for filtering bias, except that a monopolist will cull some bias for whatsoever $\alpha >0$ . The post-obit proposition summarizes these results.

Proposition 14.1

Suppose firms strategically choose distortion (filtering) biases. And then:

ane.

If α is sufficiently big and ρ sufficiently small (for all $\alpha ,\rho >0$ ), then a biased monopolist will choose $\left|b^{*}\right|\in \left(0,1\right)$ , with $\left|b^{*}\right|$ increasing in α and decreasing in ρ.

2.

In duopoly, both firms will choose $b^{*}=0$ .

3.

Consumer welfare is higher in duopoly than monopoly.

This proposition demonstrates the simple, simply important, intuition of the tradeoff a biased firm faces between political influence and directly media profit. As the importance of influence (α) increases, the firm chooses more bias, and as audience size becomes more lucrative (college ρ), the firm chooses less bias. Anand et al. (2007) and Balan et al. (2004), in addition to the papers noted below, make similar points. Moreover, the improver of simply ane competitive firm can make consumer demand infinitely bias-elastic, leading to elimination of bias in equilibrium. The proposition also implies that even rational consumers tin exist influenced past bias, every bit also shown by Jung (2009) and Adachi and Hizen (2014).

The suggestion as well implies the more subtle issue that fifty-fifty a monopolist with $\rho =0$ volition not choose maximal bias, for whatever α. Choosing total bias would amerce consumers, causing them to non consume news at all, and hence non be influenced (Gehlbach and Sonin, 2014, stress this point). The literature on supply-driven bias extends these basic intuitions in a multifariousness of ways.

Baron (2006) noted that since many news organizations are part of corporations, information technology seemed implausible that they would sacrifice profit for political bias. He showed that bias could enhance profit, however, despite the negative upshot on readership, if journalists are willing to accept lower pay when allowed to bias the news, which they might want to practice to advance their own career concerns or political preferences. In this example, it can be assisting for media owners to let even distortion bias in exchange for pay cuts. In his model, bias causes news prices to be lower due to lower demand and has an ambiguous effect on welfare as it may increase profits, but the welfare effect is negative if demand for news is loftier. With competing firms, the relation between bias and profits is ambiguous.

Anderson and McLaren (2012) report a model like ours in that media firms have preferences over consumer actions, and consumers accept homogeneous political preferences and are fully rational and sophisticated nigh equilibrium firm behavior. The media'south admission to information is exogenous, just the media can strategically withhold data (a version of distortion bias). Consumers can still be manipulated by bias since when political data is bad (from the firm's perspective), and is not reported, the consumers cannot know whether this is due to nondisclosure or the information being unavailable. Their model goes beyond ours in also because prices, the incentives of firms to merge, media costs, and allowing consumers to go news from more than one source. Consistent with our model, they observe that competition is effective in reducing distortion, and preventing mergers can improve welfare. More subtly, they note that when competing media firms have opposing biases, mergers may not occur even when allowed, due to the owners' conflicting political motives. Moreover, articulation duopoly profits can exist higher than monopoly profit, equally a single possessor with a political bias cannot credibly commit to offering diverse, differentiated news.

Chan and Suen (2009) also written report a model with rational consumers and biased outlets. Their model goes beyond ours by incorporating two-political party political competition with endogenous platforms. Voter payoffs depend on the winning party's platform and an unobserved state of the globe. The authors compare 2 cases: one in which the media but report each party'due south platform, and another in which the media reports the platforms and also makes a cheap talk report on the state. They discover that in the start instance (balanced reporting) the parties are undisciplined and choose extreme, polarized platforms, which is socially harmful. Platform convergence, which would be ideal in their model, is non an equilibrium because each party would have an incentive to deviate, and voters could non identify and punish a unilateral deviator. By contrast, in the second example of the model, the media report, fifty-fifty if biased, moderates the policies, since if ane party was to deviate and suggest a more extreme policy, then this party could be identified by voters given the media report. Greater contest enhances this moderation farther. A subtle finding is that bias does not bulldoze policy in its direction but instead polarizes candidate platforms. Since the written report is cheap talk, it is a type of distortion bias. The caste of bias is constrained non by the need to keep the audience, every bit this is exogenous, merely by the alignment betwixt the media's and public preferences.

Brocas et al. (2011) consider several variations on a simple model of media competition with biased firms. Ane novel feature they consider is that in addition to biasing its ain news, a firm tin can signal-jam a rival business firm's news, making it uninformative. Consequently, duopoly competition is not sufficient to eliminate bias. However, when there are ii firms supporting each of two "viewpoints" (political candidates), i.e., 4 firms in total, bias is completed eliminated. This is due to what they refer to as "informational Bertrand contest"—if two firms have the same viewpoint and 1 is slightly more than informative, it obtains the entire market for that viewpoint. ⁵ Hence, there cannot be an equilibrium in which one business firm tin can go marginally more than informative and capture the whole market. The authors test their model with experiments, which generally support their theoretical predictions.

The general theme of all these results is that competition will tend to reduce bias that originates on the supply side of the marketplace. Broadly speaking, competition sharpens incentives for firms to give consumers what they desire. Since supply-side distortion reduces the quality of media from consumers' perspectives, these incentives push button toward reducing distortion.

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The Theory of Decreasing Cost Production

Richard W. Tresch , in Public Finance (Tertiary Edition), 2015

Marshallian Consumer Surplus

All the same another popular approach is to assume away income effects then that the actual and compensated need curves are one and the same. In this case, Marshallian consumer surplus and the appropriate willingness-to-pay income measures such equally the HCV are identical, so there is no need to uncover the underlying indirect utility role. Assuming away income effects is hardly an attractive assumption, however. Almost all appurtenances take some income elasticity of need, and for services such equally highways and recreational facilities, it may well be substantial. The college the income elasticity of demand, the more these two do good measures volition diverge.

Yet, Marshallian consumer surplus has remained a popular measure of the value of price changes, cheers to an approximation formula due to Robert Willig. Willig demonstrated that Marshallian consumer surplus is likely to exist a close approximation of the HCV, fifty-fifty for fairly large income elasticities. Specifically, he proved that, for a single cost modify (Willig, 1976):

(9.30) $\frac{C-A}{A}\approx \frac{\eta A}{2M^0}$

where

C  =   HCV due to the price change.

A  =   Marshallian consumer surplus.

η  =   income elasticity of demand.

M ⁰  =   income in the original, no-service state of affairs.

Equally Willig points out, if the surplus (A) is 5% of full income (One thousand ⁰), even with an income elasticity (η) as loftier as 0.viii, the error in using A for C is approximately ii%, well within the range of demand estimation error.

Willig'south approximation formula is not without its bug. The assumption of a single price modify is crucial to Willig's proof. If more one price changes so that Eqn (9.26) applies, the Marshallian measure is non path dependent and is therefore not well defined. Every bit noted higher up, the single-price-alter assumption is highly suspect.

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Systems of Cities

Francisco Javier Martínez Concha , in Microeconomic Modeling in Urban Scientific discipline, 2018

Consumer Surplus

Let us analyze if consumers' surplus calibration with population. Remember that in Chapter 5 , we divers consumer surplus at the LU equilibrium equally:

(8.28) ${\overline{u}}_h=\frac{\mathrm{ane}}{\beta }\ln \left(\sum _{i\in VI}{S}_i{\left[{\mathrm{1000}}^{\prime }\frac{z_{hi}}{r_i}\right]}^{\beta }\right)$

with $z_{hi}=y_h{\mathrm{due\; east}}^{{\lambda }_h^{-\mathrm{i}}{f}_h\left(z_i\right)}$ . Supplant r _i by Eq. (eight.21),

(8.29) ${\overline{u}}_h=\frac{1}{\beta }\ln \left(\sum _{i\in \mathrm{Five}I}{S}_i{\left[\frac{z_{hi}}{{\mathrm{west}}_i{H}^{\frac{\mathrm{one}}{\beta }}}\right]}^{\beta }\right)=\frac{\mathrm{i}}{\beta }\ln \left(H^{-1}\sum _{i\in \mathrm{Five}I}{\mathrm{Southward}}_i{\left[\frac{z_{hi}}{w_i}\right]}^{\beta }\right)$

and ascertain $w^{\beta }=\frac{1}{H}\sum _{i\in VI}{\mathrm{Due\; south}}_i{\left[\frac{z_{hi}}{{\mathrm{west}}_i}\right]}^{\beta }$ to obtain:

(8.30) ${\overline{u}}_h=\frac{\mathrm{i}}{\beta }\ln \left(w^{\beta }\right)$

The principal conclusion is that utilities are constant per cluster and are independent of the city's population because rents in the denominator of Eq. (8.28) abolish the scaling effect of the number of bidders, i.e., rents extract the increase in wealth from bidders, which is transferred to land owners every bit capital letter gains. This effect is consequent with the invariance of utilities across cities in the mobility model for the population in each cluster. Information technology tin can too be interpreted as the economical caption for the bounded human attempt assumption proposed by Bettencourt (2013) because, despite the large differences in interaction opportunities between cities, in that location are no differences in expected utilities beyond intracity microzones or across cities.

The importance of the scaling results in production and wages, is that they complete our understanding of the process that generates super-linear socioeconomic outputs in cities, i.e., the link between the main causes: economies of calibration and agglomeration, with their bear on on the capitalization of profits into super-linear rents. In this process super-linear wages transfer resources from product to residents' income, which in turn transfer income into real estate and country rents.

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Consumption Externalities

Richard W. Tresch , in Public Finance (Third Edition), 2015

2 Caveats to the Pigovian Tax

The Pigovian single tax solution comes with 2 caveats. The offset caveat is the usual one of all showtime-best assay. If the government cannot achieve the interpersonal disinterestedness conditions by means of lump-sum redistributions of income, and there is no reason to suppose that it can, then a revenue enhancement equal to $-{\sum }_{h=1}^H{\text{MRS}}_{{\mathrm{Ten}}_{\mathrm{chiliad}},X_{h1}}^h$ may not be consistent with the (constrained) social optimum. We will return to this indicate in Chapter xx, which discusses externality theory in a second-best framework.

The 2d caveat is a more narrow distributional betoken. Optimally correcting for an aggregate externality with a Pigovian tax is potentially pareto superior to the initial state of affairs without the tax. Everyone can be made better off by moving to the start-best utility–possibilities frontier from an inefficient point below the frontier. But whether anybody really is better off with the Pigovian tax depends on what the government does with the tax revenues collected. The highway congestion example is a proficient example in point. The Pigovian tax is supposed to benefit the drivers on the congested highway, only the drivers could be fabricated worse off if the revenues are non returned to them, in which example the very people the regime is trying to help with the taxation will oppose it.

Figure 6.8 illustrates, equally in Fig. 6.6, D ^p is the individual market demand curve, reflecting only the private-use value of driving on the highway. D^soc is the social demand curve; it lies below D ^p at every output by the aggregate losses to the drivers on the margin resulting from the congestion. The supply bend, S _grand , assumes constant marginal cost of P _k to focus on the drivers' problem. The optimal Pigovian tax is t _k . Without a revenue enhancement, the competitive equilibrium is $(X_{\mathrm{1000}}^c,P_{\mathrm{grand}})$ , at the intersection of Due south _k and D ^p . With the optimal Pigovian tax, the equilibrium route use drops to $X_k^{\text{opt}}$ , at the intersection of S _grand and D^soc. The price to the drivers rises to P _thou  +t _thousand , and the taxation revenue collected from them is $t_k{X}_m^{\text{opt}}$ .

Figure vi.8.

Assume no income effects and so that consumer surplus is an appropriate income mensurate of the drivers' welfare. The potential consumer surplus at whatsoever output is the area between D ^soc and S _k to that output. At the no-tax equilibrium ${\mathrm{10}}_{\mathrm{yard}}^c$ , the drivers' consumer surplus equals areas 1 + 2   –   4. Area four represents the loss caused by excessive congestion at the no-revenue enhancement equilibrium. At the pareto-optimal output Ten ^opt, the potential consumer surplus available to the drivers equals area 1 + 2, but the drivers obtain this surplus merely if the tax acquirement, equal to area two + 3 is returned to them. The drivers are clearly better off at $X_k^{\text{opt}}$ if they receive the taxation revenue; they avert the excessive congestion at the no-taxation equilibrium, represented by area 4. If the tax revenue is not returned, notwithstanding, the drivers' actual consumer surplus is only surface area 1–3. Whether they are now amend off at X ^opt depends on the relative size of areas 1 + 2 – 4 and ane–3. If the taxation revenue (2 + 3) exceeds surface area iv, the drivers are worse off at the optimum and they will resist the taxation. ¹⁵

This assay may explain why commuters tend to resist tolls that are intended to reduce highway congestion by diverting some of them to other means of transportation. The commuters know that they will not receive the cost acquirement. In their view, they will just confront higher commuting costs that exceed the value to them of the reduced congestion.

We should note that this second caveat is not entirely consistent with the first-best policy assumptions. First-all-time assay assumes that the authorities engages in allocational policies to bring society to the first-best utility possibilities frontier and that it redistributes lump-sum to reach the bliss signal on the borderland. The caveat ignores the distributional function of the policy. Whether the drivers are better or worse off at the bliss indicate ultimately depends on society's social welfare rankings and the interpersonal equity conditions that are derived from them. The disposition of Pigovian revenue enhancement revenues may be taken into consideration by the government when it redistributes, but information technology is irrelevant to determining the final distribution of income. Nonetheless, resistance to tolls and other forms of externality taxes is quite song, perhaps because people do not believe that the authorities has a fully articulated distributional policy. Therefore, they react more to their direct gains and losses from the government's allocational policies than to the efficiency gains from the policies.

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How do consumers reply to real income shocks?

JPMorgan Chase Establish , in Handbook of United states Consumer Economics, 2019

Abstract

How much exercise income fluctuations touch on consumers' welfare? The permanent income hypothesis posits that a family unit's consumption changes in response to changes in lifetime income simply not transitory or predictable fluctuations. The JPMorgan Chase Constitute has assembled high-frequency, categorized data on income and expenditure for millions of households, which allow u.s. to describe the impacts of specific fluctuations in income (a revenue enhancement refund and a chore loss) and prices (fuel prices and mortgage interest rates) that vary in terms of predictability and elapsing. Nosotros find spending responses to changes that were predictable or had limited bear upon on lifetime income. We identify spending changes in response to new data versus the cash menses event itself and in specific categories of consumption where consumers would likely prefer timing to be driven past needs rather than greenbacks period, such as healthcare. Our findings suggest that frameworks which rely on rational expectations and intertemporal optimization are of express usefulness for understanding consumer behavior or designing policies and financial product offerings.

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Social Construction of Preferences

Jess Benhabib , Alberto Bisin , in Handbook of Social Economics, 2011

three.ii Ad and welfare

Studying the effects of advertisement on consumers' welfare is not straightforward because, as advertisement changes consumers' preferences, it is not at all obvious what the reference welfare criterion should exist, ex-ante or ex-post with respect to ad. ¹²

Given the preference parameters α, θ, b (we use for simplicity a notation which abuses by postulating symmetry), the representative consumer'due south equilibrium allocations are denoted by 10(α, θ, b), Fifty(α, θ, b); and his/her equilibrium utility is denoted $\mathcal{U}(x(\alpha ,\theta ,b)$ , Fifty(α, θ, b); α, θ, b). Call up that advertising has the effect of changing his/her preference parameters (α, θ, b) into (α ₊, θ ₊, b ₊).

We say that the consumer'south welfare (weakly) increases due to advertising with respect to ex-mail service preferences if

(half dozen) $\mathcal{U}(x({\alpha }_{+},{\theta }_{+},b_{+}),\mathrm{50}({\alpha }_{+},{\theta }_{+},b_{+});{\alpha }_{+},{\theta }_{+},b_{+})\ge \mathcal{U}(\mathrm{ten}(\alpha ,\theta ,b),\mathrm{50}(\alpha ,\theta ,b);{\alpha }_{+},{\theta }_{+},b_{+}).$

Consumer's welfare (weakly) increases instead due to advertising with respect to ex-dues preferences if

(7) $\mathcal{U}(x({\alpha }_{+},{\theta }_{+},b_{+}),L({\alpha }_{+},{\theta }_{+},b_{+});\alpha ,\theta ,b)\ge \mathcal{U}(\mathrm{ten}(\alpha ,\theta ,b),L(\alpha ,\theta ,b);\alpha ,\theta ,b).$

Several ^thirteen of our welfare comparisons are in fact unambiguous, in the sense that they hold for the fractional ordering induced past both ex-ante also as for ex-mail service preferences. In an economic system in which prices are distorted by monopoly power of firms, in fact, advertising might, depending of the parameters of the economy, either exacerbate such effects, and hence possibly reduce welfare with respect to both ex-ante and ex-post preferences, or it might innovate a form of nonprice contest across firms which mitigates the effects of monopolistic distortions and hence on the opposite unequivocally improves welfare.

How does advertising affect the welfare of the representative agent? We over again consider separately the furnishings of the unlike advertising channels, intensity on α, elasticity of substitution on θ, and habits on b.

1.

Advertising on α, other things equal, decreases (resp. increases, has no consequence on) ex-post welfare if σ < 1 (resp. if σ > ane, σ = 1) since it uniformly decreases (resp. increases, has no effects on) utility levels. Furthermore, if |α ₊ − α| is loftier enough, the representative consumer's welfare decreases with respect to ex-ante preferences (a moderate increment in α increases only moderately the labour supply, 50, thereby possibly reducing the distortion towards leisure that is induced by monopolistic competition).

two.

Advertizement on θ, other things equal, reinforces whatsoever result of advertising on intensity α. However, advertizement on θ has also the effect of increasing the price p ₊. The price effect ever accentuates the negative welfare consequences of monopolistic contest; more and so in the economy with costless entry, where profits are not redistributed to consumers simply rather wasted in expanding varieties.

3.

Advertising on b, other things equal, reduces ex-ante welfare only has cryptic welfare results with respect to ex-post preferences.

Let'south report once again the special case of log preferences (σ = 1), when income and substitution effects cancel out:

1.

log Advertizing on α, other things equal, has no effects on ex-mail service or ex-ante welfare.

2.

log Ad on θ, other things equal, has the effect of increasing the price p ₊. The price effect has negative welfare consequences.

3.

log An increase in b, other things equal, reduces ex-ante welfare but has ambiguous welfare results with respect to ex-mail preferences.

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Handbook of Health Economics

Dana Goldman , Darius Lakdawalla , in Handbook of Health Economics, 2011

four.i The Uncomplicated Normative Theory of Market Exclusivity and Innovation

Define E(CS|D ) as expected consumer surplus in the discovery land and E(CS|N) as expected consumer surplus in the no-discovery country. The canonical model then implies the post-obit social planner's trouble:

${\text{max}}_{I}p(I)\mathrm{Eastward}(C\mathrm{Due\; south}|D)+(1-p(I))E(CS|\mathrm{North})-(\mathrm{one}+r)I$

The planner'southward problem has the following showtime-order condition:

$p΄(I)[\mathrm{Eastward}(C\mathrm{South}|D)-\mathrm{East}(CS|\mathrm{North})]=(\mathrm{one}+r)$

Private incentives will be perfectly aligned with public incentives, so long as:

$\begin{array}{l}\varphi (I)=I\\ \mathrm{East}(\mathrm{\pi }|D)-E(\mathrm{\pi }|N)=E(CS|D)-E(CS|N)\end{array}$

Efficiency in the canonical model requires that the innovator conduct the full price of the innovation outlay, and exist able to appropriate the entire marginal social value of his invention. The latter is equal to the total increment in consumer surplus generated by the new discovery.

Developing the normative implications further requires clarity around the "ex post" period in which profits are earned. The near common circumstance is 1 in which the innovator (or her licensee) enjoys a monopoly on the sale of all goods connected with the new invention. In the no-discovery state, we can call back of the firm as a standard competitor, in which profits are equal to zero. A monopolist with access only to a linear pricing instrument volition never be able to appropriate the full measure of consumer surplus.

This problem is fabricated even more acute in the instance of goods sold to healthy people, such every bit vaccines (Kremer and Snyder, 2006). Vaccines are sold before consumers know their ultimate illness status and while there is still private data virtually infection risk. Drugs to treat disease, on the other hand, are sold to sick people exclusively, when in that location is no longer private information almost illness run a risk. The existence of individual information creates heterogeneity in willingness-to-pay: individuals who face college risk of infection are willing to pay more, and vice versa. This heterogeneity makes it harder to extract the full measure of consumer surplus. In the farthermost instance of homogeneous willingness-to-pay, for example, a manufacturer with monopoly ability could excerpt all available consumer surpluses in the form of a compatible, linear cost. Notably, this type of reasoning would utilise, albeit in weakened form, to drugs that treat illness, but also serve equally secondary prevention. For example, treatments for diabetes besides forbid ophthalmologic complications, amputation, and other sequelae of the disease. Individuals may take private data well-nigh their predisposition to any or all of these potential complications; this can impact their willingness-to-pay in a similar way.

The statement in a higher place should not exist taken to imply that perfect cost discrimination is always possible for a treatment. Indeed, individuals vary in their severity of illness and willingness-to-pay for treatment. Nonetheless, the of import bespeak is that vaccines are sold to markets with an additional dimension of heterogeneity, making it correspondingly more than difficult to excerpt the total mensurate of consumer surplus.

In sum, information technology will be true that

$E(\mathrm{\pi }|D)-E(\mathrm{\pi }|\mathrm{North})<E(CS|D)-\mathrm{East}(CS|N)$

This leads to the underprovision of innovation. Moreover, monopoly power in the event of discovery leads to underprovision of the adept that embodies the new thought. The canonical model thus predicts the being of too petty innovation investments, too few new discoveries, and too little dissemination of the new appurtenances discovered.

These two problems are complementary, in the sense that 1 cannot hope for first-best innovation in the presence of 2nd-best provision. For example, suppose i were to aim for efficient innovation investment by subsidizing investment. It would appear that the optimal policy would be to construct a subsidy such that:

$\begin{array}{l}\varphi ΄(I)<\mathrm{i}\\ \frac{E(\mathrm{\pi }|D)-E(\mathrm{\pi }|\mathrm{Northward})}{\varphi ΄(I)}=E(CS|D)-E(CS|N)\end{array}$

Withal, note that the presence of monopoly provision of the good lowers the consumer surplus that is actually achieved past that adept. Therefore, at best, we can achieve a second-best level of innovation that is optimal, relative to the new, lower level of consumer surplus. Policy approaches that tackle both problems simultaneously are thus preferable.

The statement for underprovision of innovation relies on the inability of the innovator to capture the total value of social surplus. Several papers in the literature have empirically examined the charge per unit at which innovators advisable total social surplus. Nordhaus (2004) examines a range of innovations—not just in the pharmaceutical industry—from 1948 to 2001. He concludes that innovators capture 2.2 percent of total present value to society of their inventions. Nordhaus bases his approach on a calibrated model of demand, consumer surplus, and profit. A key assumption is the linear pricing of inventions, and the "appropriability ratio," or the extent to which innovators can harvest consumer surplus given the type of demand curve they face.

An appropriability estimate specific to the pharmaceutical literature is that of Philipson and Jena (2006). They consider the case of HIV treatments, where they judge that approximately 5 percent of the social surplus is appropriated by innovators. They calculate social surplus using estimates of survival increase implied by the new treatments, and then valuing these using an economic framework for the willingness-to-pay for survival gains. They too recognize, nevertheless, that the instance of HIV handling is unique, in the magnitude of social value generated. Equally a upshot, they have a broader view, using a database reporting cost-effectiveness ratios for more 200 drugs. This database allows them to approximate survival gains for all these drugs, and value these using an economic framework. The rate of cribbing is lower for HIV drugs, just they argue that the general rate of appropriation in the pharmaceutical manufacture remains depression—around ten percent of total social value generated.

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The Stochastic Bid-Auction State-Use Model

Francisco Javier Martínez Concha , in Microeconomic Modeling in Urban Science, 2018

The Multinomial Logit Choice Model: Consumer Surplus Arroyo

The selection model can also be derived by maximizing the consumer surplus. Under the supposition of the i.i.d. Gumbel willingness to pay, the consumer surplus is defined by:

(four.12) $c{s}_{hi}=w_{hi}-p_i$

Because the consumer is assumed to exist a price taker, i.east., the asking cost p _i is exogenous and known to the consumer, the consumer's surplus preserves the i.i.d. Gumbel distribution of the willingness to pay with shape parameter β _h   = λ _h μ _h , although the location parameter is displaced to the left in p _i .

In this context, the maximum consumer surplus or option model is represented by the post-obit MNL probability:

(iv.13) $P_{i/h}=\frac{e^{{\beta }_h(w_{hi}-p_i)}}{{\sum }_{j\in \mathrm{Five}I}{e}^{{\beta }_h(w_{hj}-p_j)}}$

which besides admits an aggregated version such as Eq. (iv.8). As expected, the pick probability increases with the willingness to pay and decreases with prices.

To empathize why this choice procedure yields maximum utility, it is worth recalling that willingness-to-pay values across the set of alternative locations are set such that they yield the same reservation utility, i.e., west _hello (u _h ), ∀ i  ∈ VI, and therefore, the consumer is indifferent to choosing any location if the price equals the willingness-to-pay value. It follows that at the location where the willingness to pay is beneath the asking toll, at that place is a gain in utility with respect to its reservation value and where the price is college, in that location is a loss. So, maximizing gains implies maximizing utility and the consumer surplus.

The expected maximum consumer surplus of a gear up of options VI with i.i.d. Gumbel distributed variates is calculated equally:

(4.14) $c{\mathrm{south}}_h^{\ast }=\frac{1}{{\beta }_h}\ln \left[\sum _{i\in \mathrm{Five}I}{\mathrm{eastward}}^{{\beta }_h({\mathrm{west}}_{hi}-p_i)}\right]+\frac{\gamma }{{\beta }_h}$

and the maximum consumer surplus is also a Gumbel variate with parameters (η _h ,β _h ) and mode ${\eta }_h=\frac{\mathrm{ane}}{{\beta }_h}\ln \left[\sum _{i\in 5I}{\mathrm{east}}^{{\beta }_h(w_{hi}-p_i)}\right]$ . In this case, considering the consumer surplus has the dimension of income, so $\frac{\gamma }{{\beta }_h}$ is meaningful not but statistically but also economically.

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