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Chapter 5: Efficiency and the Role of Government “According to the system of natural liberty, the sovereign has only three duties to attend to ... first, the duty of protecting the society from the violence and invasion of other independent societies; secondly, the duty of protecting, so far as possible, every member of the society from the injustice or oppression of every other member of it, or the duty of establishing an exact administration of justice, and thirdly, the duty of erecting and maintaining certain public works and certain public institutions, which it can never be for the interest of any individual, or small number of individuals, to erect and maintain” Adam Smith The Minimum Role of Government (Laissez Faire) According to Adam Smith, the fundamental roles of government include national defense, an impartial system of laws, a set of public works and institutions which can’t be maintained by individuals, such as roads Government in Perfect Competition Any change from a Pareto optimal situation is likely to produce a loss of efficiency, including the actions of government. Efficiency Concepts in an Economy with Government Definition: Government Surplus (GS) = the net benefits of the market to government = government tax revenue- government spending. Concept: The net benefits in a market with government include government surplus as well as others. Net Benefits = Consumer Surplus + Producer Surplus + Government Surplus + External Surplus Taxes are positive gains for government, and government spending is a loss for government. A Tax on Producers Cuts Supply by Increasing Cost After a constant per-unit tax is imposed, • Consumer Surplus Falls to A. • Producer Surplus Falls to H + I. • Government Surplus (tax revenue) rises from nothing to B + D. • Net Gains Fall because C and E are lost. Table 5-1: The Efficiency Effects of a Constant Per-Unit Tax Market Condition No Tax With Tax Difference Consumer Surplus A+B+C Producer Surplus D+E+H+I Government Surplus None A -B -C H+I -D-E B+D B+D Net Gain A+B+C+D+E +H+I A+H+I+B+D -C-E Deadweight Loss None C+E C+E A tax on Consumers has very similar effects • A tax on consumers creates two demand curves. • The original curve gives the maximum willingness to pay. • The new demand subtracts the amount of tax from willingness to pay, giving the new relation between price and quantity. • Quantity falls, just as with a producer tax • Price falls, but consumers pay tax separately • Consumer Surplus falls to A • Producer Surplus Falls to H • Govt. Surplus is B+D. • Net gains fall by C and E • C and E are the deadweight loss Producer vs. Consumer tax If the demand and supply curves are the same, producer and consumer taxes have the same effect on the market. Consumers pay more (including any tax), producers keep less revenue for each unit sold, quantity falls, and a deadweight loss occurs. The Effects of a Fixed per-unit Subsidy A subsidy is the opposite of a tax in several ways 1) Government loses money and will have a negative government surplus. 2) Consumers and Producers are both likely to gain from a subsidy compared to the competitive market. 3) If applied to a perfectly competitive market, subsidies encourage overproduction rather than underproduction. 4) Subsidies are likely to be politically popular among those groups who receive them, unlike taxes. The Effects of a Fixed per-unit Production Subsidy • Because producers receive revenue from the government and also from consumers, consumers will pay less than producers receive in revenue. • Consumer Surplus grows due to the lower price and higher quantity. • Producer Surplus grows because of the higher revenue per unit they receive and the higher quantity. • Government Surplus is negative because it is subsidizing the private sector. • Area I is the deadweight loss because it is the only part of the government subsidy that doesn’t benefit producers or consumers The Effects of a Fixed per-unit Subsidy Table 5-2: The Efficiency Effects of a Constant Per-Unit Subsidy Market Condition No Subsidy Subsidy Difference Consumer Surplus A+B A+B+C+D+E C+D+E Producer Surplus C+F B+H+C+F B+G Government Net Gain Surplus None A+B+C+F -B-H-I-C-D-E A+B+C+F-I -B-H-I-C-D-E -I Deadweight Loss None I I The Effects of a Quota (a limit on quantity bought and sold) A quota has effects similar to a monopoly • Higher price • Lower quantity • Price is greater than the marginal cost of production. • A deadweight loss due to underproduction. Table 5-3: Effects of a Quota Market Condition No Quota Quota Difference Consumer Surplus A+B+C A -(B+C) Producer Surplus D+E B+D B-E Government Net Gain Surplus None A+B+C+D+E None A+B+D None -(C + E) Deadweight Loss None C+E C+E The Effects of Price Floors and Ceilings • If effective, price floors and ceilings produce disequilibria (production shortages or surpluses). • Either buyers or sellers definitely lose. • Both policies produce an under-production deadweight loss of C+E. Table 5-4: Price Floors and Ceilings Market Condition Consumer Surplus Producer Surplus Government Surplus Net Gain Deadweight Loss Competition A+B+C D+E+F None None Price Ceiling Price Floor A+B+D A F B+D None None A+B+C+D+ E+F A+B+D+F A+B+D C+E C+E Agricultural Policy: Alternative Strategies Is there any market failure you can think of that would justify the subsidization of agriculture on efficiency grounds? There have been several types of policies for subsidizing agriculture in different nations. Agricultural Policy: Price Floor Policies • A policy that includes buying surplus grain is much less efficient than paying farmers not to grow because the cost of growing the grain is wasted. Table 5-5: Alternative Price Floor Policies Policy Competitive Market Price Floor: Govt. buys the surplus Price Floor: Pay farmers not to grow beyond Q Consumer Surplus A+B+C Producer Surplus G+F Governme nt Surplus None A B+C+D +G+F -(C+D+E B+C+D+G +F+E+I -(C+D+E A Net Gains A+B+C +G+F A+B+G-E-I Deadweight Loss None C+F+E+I +F+I) +F+I) A+B+G C+F Quotas and Subsidies Quotas and Subsidies have been applied to agricultural markets. Their general effects are expected to be the same as those in our models. Quotas will raise the price and lower the quantity, but will not involve any payments to farmers for excess grain Subsidies will increase production, lower consumer prices, raise producer surplus, and cost the government money. Summarizing Alternative Agricultural Programs Table 5-6: The Efficiency Effects of Alternate Agriculture Programs Policy Competition Price Floor + Govt. Buys Surplus Price Floor + Govt. pays not to grow Quota Subsidy Consumer Surplus A+B+C Producer Surplus G+F+J Government Surplus None B+C+D+ G+F+J B+C+D+ G+F+J+ E+I+L -C-D-EF-I-L -C-D-EF-I-L A B+G+J A+B+C+G +F+H+I B+C+D+ G+F+J A A Net Gain A+B+C+ G+F+J A+B+G+J -E-I-L Deadweight Loss None C+F+ E+I+L A+B+G+J C+F None A+B+G+J C+F -B-C-D-E -F-G-H-I A+B+C+ G+F+J-E E Government and Imperfect Markets Can two “wrongs” make a right? Taxing Negative Externalities • An optimal Pigou tax can eliminate overproduction and reduce the negative externality. • Both consumers and producers lose, however. Table 5-7 (from Figure 5-9): A Tax on a Polluting Market Private Equilibrium With Tax CS ABCD A PS EFGKLM KLM External S. -(MFCDGH) -CFM Govt. S. None BCEF Net Gains ABEKL - H ABEKL An Extended Example: A Pollution Tax with Numbers marginal private cost = 10 + Q marginal social cost = 10 + 1.5 Q demand P = 100 – Q Step 1: Find social equilibrium Price and Quantity Step 2: Find the private marginal cost at the same quantity , and the difference between the private and social MCs An Extended Example: A Pollution Tax with Numbers marginal private cost = 10 + Q marginal social cost = 10 + 1.5 Q demand P = 100 – Q Step 1: Find social equilibrium Price and Quantity Qsocial = 36, P = 64 (from demand curve) Step 2: Find the private marginal cost at the same quantity , and the difference between the private and social MCs MCprivate = 10 + 36 = $46 MCsocial = 10 + 1.5 (36) = $64 Difference = $18 = the marginal external cost at that quantity The Policy: Impose a per-unit tax equal to the marginal external cost at the social equilibrium Imposing an $18 tax per unit shifts the private MC upward by $18, to… Private MC + tax = 28 + Q The new private equilibrium with the tax will be 100 – Q = 28 + Q The new quantity = 36, and the new price = 64 Calculating the Net Gains for all parties: CS, PS, and GS CS = ½ x 36 x ($100 – 64) = $648 GS (tax revenue) = $18 x 36 = $648 PS = ½ x 36 x ($46 - $10) = $648 External Surplus (ES) equals area C+F+M+I minus area I: External Surplus = – [½ x 36 x (64-10) - ½ x36 x (46-10)] = - $324. Total net gains = CS + PS + GS + ES = $648 + $648 + $648 - $324 = $1,620. Compared to the Private Equilibrium: At the private equilibrium, Q = 45, P= 55 CS = 1,012.5 PS = 1,012.5 Ex. S. = -506.25 Net Gains = 1,518.75 At the social equilibrium, Q = 36, P = 64 CS = 648 PS = 648 GS = 648, Ex. S. = - 324 Net Gains = 1620 $101.25 of deadweight loss has been eliminated (area H in Figure 5-8) Negative externalities have been reduced Consumers and producers are worse off Price Ceilings and Natural Monopoly A “Natural Monopoly” has high economies of scale, and therefore has a falling average total cost over much of its range. If unregulated, it will produce too little (recall that the social equilibrium would Be where demand = Marginal cost) and charge a high monopoly price. A price Ceiling changes the relationship between Price and Marginal Revenue for a Monopoly Table 5-8: No Price Ceiling PRICE Quantity Total Revenue Marginal revenue 10 2 9 3 8 7 4 5 6 6 5 7 4 8 xxx • If the Marginal Cost is Fixed at $3, how much will be produced in each table? Table 5-9: Price Ceiling at $6 PRICE 6 6 6 6 6 5 4 Quantity 2 3 4 5 6 7 8 Total Revenue Marginal xxx revenue Different Price Cap Policies If the price cap is set where Demand = ATC, the monopoly will produce Q1 and will make zero economic profits (because price = ATC) But some deadweight loss will remain. If the price cap is set where Demand = MC, The monopoly will produce Q2 and reach an Efficient outcome, but will have negative profits because Price is less than ATC. States regulate utilities using versions of the average cost approach. Public Choice and Government Failure Public choice theory uses the concepts of self-interest and competition to analyze the behavior of voters, politicians, interest groups, and bureaucrats. Two Categories of Public Choice Theory The “Virginia School”: Self-interested voters, politicians, and interest groups create multiple layers of problems that limit the ability of government to translate a society’s preferences into effective policy. The “Chicago School”: Government policies tend to evolve into rational responses to market imperfections and injustice The limits of Social Welfare Functions The social welfare function defines society’s well-being as a function of the utility of its individual citizens. SWF = f(U1,U2,…,UN), where U1 is the utility of individual 1, etc. Different ethical theories have different weights for individual utilities Since utility is generally not measurable it can’t be directly added or compared across individuals. Voting and Elections Arrow’s Impossibility Theorem The Median Voter Model Interest Groups and “Rent Seeking” Arrow’s Impossibility Theorem An effective rule for collective decisions must meet the following criteria: 1. The rule leads to a decision regardless of the form of voters’ preferences. 2. The rule can provide a societal ranking for all possible outcomes. 3. The rule must be consistent with individual preferences. 4. The rule is transitive. 5. Society’s ranking of any two choices must be independent of other alternatives. 6. Dictatorship is not permitted. Arrow’s Impossibility Theorem Arrow’s Impossibility Theorem: It is impossible for a collective decision rule, including elections, to meet all six of these conditions. Arrow’s Paradox: The only collective choice mechanism that is always transitive and allows for consistent preferences over all choices is dictatorship The Median Voter Model In a simple yes or no or two-party vote the outcome of the median voter model reduces to majority rule. If voter preferences are not distributed in a normal distribution (with “single peaked preferences”) the election result may not produce a policy favored by a majority. Table 5-10: A Distribution of Spending Preferences PROPOSAL Number of voters 50 % SPENDING INCREASE 20 % SPENDING INCREASE NO SPENDING INCREASE 20 % SPENDING CUT 50 % SPENDING CUT 3,500 1,000 1,000 2,500 2,000 total = 10,000 In Table 5-10 the median voter favors no spending increase, but 9/10 of all voters favor a different policy. Interest Groups and “Rent Seeking” Rent seeking takes place when an organization uses political donations, public relations, or lobbying efforts to gather benefits from government. For a firm or industry, rent seeking activity is rational if the net benefits of governmental activity outweigh the benefits of investment in productive activity. Rent Seeking biases the political process and diverts funds from socially productive uses. A political interest group that relies on membership may organize through persuasion or offers of services, and then use member’s contributions to pursue political activities. Administration The administration and enforcement of laws and programs are the duties of the government’s bureaucracy. The goals of administrators may not be consistent with the public interest. One model of bureaucracy hypothesizes that the goal of the bureaucrat is to maximize her agency’s discretionary budget, which is the difference between total revenue and the minimum cost of producing the agency’s expected output. If oversight is lacking government services are likely to be too small in scale and too expensive relative to the efficient ideal, much like the effects of a monopoly Regulatory Agencies and Capture Theory According to Capture Theory, businesses in regulated industries may be able to control the setting of prices or enforcement of rules by rewarding the regulator for actions favorable to the firms or by controlling information about costs in a way that leads to favorable judgments. However, oversight by the public and the legislature provides a possible controlling mechanism for interest group power over regulators. Enforcement The role of financial punishment in law enforcement can be viewed through a relatively simple concept known as the expected fine. The expected fine equals the odds of being found guilty of a violation times the fine if convicted. In symbols, EF = π•F; where EF is expected fine, π (the Greek letter pi) is the probability of being convicted and F is the fine if convicted. If the fine or the odds of being convicted are very low, the expected fine will also be low, and the incentive to follow the regulation or law will be small. An Enforcement Example Your Turn 5-5: Using the expected fine formula, if the average firm has a .02 chance of being inspected by OSHA and faces a $400 average fine if inspected, what is the average expected fine? (Hint: You probably have more in your wallet). Conclusion The main goal of this chapter is to review the economic rationale for the role of government in an economy. When markets are inefficient a window of opportunity exists for improved efficiency through public policy. Mathematically, this chapter provided further examples of the marketbased mathematical topics introduced in Chapters 2 and 4.