Social Optimum vs Competitive Equilibrium

• The content provides a study of a closed-economy, one-period macroeconomic model.
• The model includes 3 agents: the consumer, the firm, and the government, in 2 markets (goods and labor)
• It looks at competitive equilibrium along with its effects on Pareto optimality
• It covers comparative statics, distorting taxes, and the Laffer curve.

Introduction

• The goal is to use the representative consumer and representative firm models to build a macroeconomy model.
• Focus lies on consumers and firms within a closed economy.
• A closed economy has no trade or interaction with other countries, where an open economy does.

Government

• Many macroeconomic models have government involvement.
• The government purchases consumption goods, G, and it finances this through taxes on consumers.
• The government operates under the constraint that its budget, G, equals taxes, T, in real terms.

Competitive Equilibrium

• The economy is said to be in "equilibrium" when all consumer and firm actions are mutually consistent.
• With consistency, demand equals supply at market prices.
• A "competitive" firm or consumer is a price-taker.
• Balance between demand and supply signifies that the market clears.
• Exogenous variables determine the model, and it is used to determine endogenous variables and how they change.
• Several conditions define a competitive equilibrium, given exogenous variables:
• Consumers maximize utility through optimizing consumption C and labor supply Ns, given labor rates w, taxes T, and dividend income π.
• Firms optimize profits by selecting labor demand Nd, given productivity z and capital stock K.
• The firms profits equal the consumers dividend income.
• The labor market clears: Ns = Nd
• The goods market clears: Y = C + G
• The government maintains a balanced budget constraint to satisfy: G = T
• Walras's Law implies that the goods market clears (#5) if the other conditions are met.
• An important characteristic of competitive equilibrium is that it is Y = C + G.
• The income-expenditure identity, recalling the GDP measurement chapter, is Y = C + I + G + NX.
• With this model NX = 0 since it is a closed economy, and I = 0 because there are no dynamics. (Investment expenditures are for the future.)
• There exist various analytical methods for working with such economic models: algebraic, numerical, and graphical.

Graphical Approach to Competitive Equilibrium

• Equilibrium is where consumer and firm decisions are consistent.
• An equilibrium relationship arises between the amount of labor the representative employer uses and aggregate output.
• The production possibilities frontier (PPF) is the technological relationship between C and l (leisure), found by shifting the relationship in (b) via the amount G.
• Consumption bundles exist within a feasible technological level to produce within the shaded region.
• The negative of the PPF slope, called the marginal rate of transformation, tells the conversion rate between leisure and consumption.
• Equilibrium occurs where consumer preferences and production technology align.
• Equilibrium bundles are demonstrated where the slope of the budget constraint, AD, which is faced by the consumer, equals the minus real wage.

Equilibrium Conditions

• The overall equilibrium condition requires that MRSI,C = MRTI,C = MPN, where consumer and firm behavior are aligned.
• In equilibrium the consumer and firm face the same market real wage.

Optimality

• Socially optimal outcomes are equivalent to outcomes that are Pareto-optimal.
• Pareto-optimal equilibria is achieved when the movement of any resources or reallocation of goods does not make someone any better off without making someone else worse off.
• Pareto-optimality implies maximizing the utility of the representative consumer, in a representative consumer setup
• Because free markets can deliver socially optimal results, Pareto optimal outcomes are often easier to attain.
• If the social planner is benevolent they choose quantities to improve consumer well-being.

Social Planner's Problem

• The social planner seeks to improve the representative consumer’s utility
• The equation is as follows: max C,I U(C, I) subject to C + G = Y; Y = zF(K, h − l); C ≥ 0; and 0 < l < h
• Welfare theorems state that, a competitive equilibrium is Pareto optimal, and, a Pareto optimum is a competitive equilibrium under certain conditions.
• It is easier to solve for Pareto optimum as opposed to competitive equilibrium.
• Several factors can disrupt the efficiency and societal optimality in a market economy, including externalities, distorting taxes, and the existence of monopolistic behavior.
• The relationship MRSI,C = MRTI,C tends to break if social benefit does not equal social costs.

Comparative Statics

• Increase in government spending effects:
• With an increase in government spending, consumption and leisure for the consumer will decrease, due to the income effect.
• Because of this, employment and quantity of output will both increase.
• AG 0 crowds out consumption, and AC < 0.
• An increase in G leads to an increase in employment, however, the real wage decreases.
• Since competitive equilibrium is Pareto-optimal, we leverage social planner's problem to maximize results.
• With an increase in total factor productivity (z), what happens to endogenous variables?
• More employment has occurred, so the output has increased.
• With any quantity of leisure consumed, more consumption can be met.
• When the number of hours worked is increased, workers have more income, C↑ and / ↑
• There is ambiguity on the effect on leisure. The income or substitution effect dominates the ambiguity.

Interpretation of Effects

• The interpretation of an increased effect depends on whether the time period is long or short.
• In the long run we are capturing years, and in the short run months, quarters, and years.

Distorting Taxes

• A distorting tax has taxes which distort allocation of resources by changing relative prices and/or supply and demand.
• A distorting tax means that the competitive equilibrium is not Pareto-optimal.
• Fiscal policy effects are of interest, including the effects of income tax.
• A proportional tax on wages is the distorting tax.
• The model includes the parameters of consumer, firm, and government agencies.

Simplified Model via Proportional Income Taxation

• Revenue is used for governmental expenditure
• C = w(1 – t)(h − 1) + π is representative consumer’s budget constraint.
• G = wt(h – 1) which means that the tax revenues are given by the government's expenditure.
• The representative firms profits are zNd – wNd = (z - w)Nd
• (z - w) is the profit that the firm makes for each unit of labor input.
• With no profits it does not matter how the labor is hired.
• Labor has an infinitely elastic factor on wage w = z.
• PPF (production possibility frontier) can therefore function as a straight line denoted AB.
• In contrast to the Pareto-optimum, the competitive equilibrium occurs at point H.
• And the economy isn't socially efficient as a result.
• With a proportional tax the sense in private decisions is disrupted due to the tax distortions.
• Government revenue comes when the government tries to maximize G, using tax revenue at income t with the equation REV = tz[h − 1(t)]
• It is possible for tax revenue to go down as t increases, if tax base is reduced.
• The function of quantity of tax revenue is given by the Laffer curve.

Laffer Curve

• The curve AB is the Laffer curve and can show the quantity of generated tax revenue.
• For how the government needs government expenditures balanced you can show G = tz[h − 1(t)] equation.
• If t =1 or 0. there will be no money being raised from that government.
• When revenue can be maximized by setting t=t*
• The government will be either on the good side or the bad depending whether it is wishes to be balanced.
• With two ways for tax rates, for any government, at which time to let see ce as more Multiple Equilibria
• With two possible ways for any given G, we should look at how the CE functions.
• At a given point for low vs high rates
• Lower leisure is observed and with more equilibrium with tax rates
• If is it is a higher indifference at a top curve.
• Low rate tax are more the consumer is better in 1 equilibrium that at it that there can become too rate at tax.

Explore the preference for social optimum over competitive equilibrium. Examine the objective of a social planner in constrained optimization and the meaning of Pareto-optimality. Also, consider the government's budget constraint in a closed economy.