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ECON 2400
Wai Ming Ho

AP/ECON2400A (Fall 2012) W.Ho Example 5: A competitive equilibrium with distortionary taxes Consider a one-period, closed economy consisting of a large number of identical con- sumers, a large number of identical ▯rms, and a government. Each economic agent acts as a price taker in perfectly competitive markets. The economic behaviors of the consumers and ▯rms are as described in Example 3 with the following modi▯cations. ▯ The consumers faces a labor income tax rate, t, instead of the lump-sum tax, T. ▯ The production function is linear in labor and does not need capital input, Y = zN. Questions: 1. Illustrate how the ▯rm determines the optimal labor demand and output supply deci- sions. What is the condition that has to be satis▯ed? 2. Write down the budget constraint of the consumer. 3. Illustrate how the consumer determines the optimal consumption and leisure decisions. What is the condition that has to be satis▯ed? 4. What are the four conditions that a competitive equilibrium must satisfy for this economy? 5. Draw a diagram with the PPF to illustrate the Pareto optimal allocation. 6. Illustrate why the competitive equilibrium of the economy is not Pareto optimal. AP/ECON2400A (Fall 2012) W.Ho { Example 5 2 Answers 1. The ▯rm’s real pro▯t is ▯ = Y ▯ wN = zN ▯ wN. The ▯rm’s optimal labor demand will be perfectly elastic at w = MN = z, and its optimal pro▯t is zero, ▯ = 0. 2. Given the labor tax rate t, the consumer’s budget constraint is C = (1▯t)w(h▯l)+▯. From question 1, we have ▯ = 0, and the consumer’s budget constraint becomes C = (1 ▯ t)w(h ▯ l): 3. The objective of the consumer is to maximize U subject to C = (1 ▯ t)w(h ▯ l): The consumer tries to achieve the highest feasible level of utility. Given that the indi▯erence curves are downward sloping and convex, the optimal consumption bundle (point H) is given by the point where the budget constraint is tangent to an indi▯erence curve. H At this point, we have the condition, MRSl;c= w(1 ▯ t): (See Figure 1) Figure 1: Optimal consumption-leisure choice C 6 budget line w(1 ▯ t)h rslope=▯w(1 ▯ t) @ @ @ @ @ C▯ @r @ @ indi▯erence curve @ slope=▯MRS l;c @ @ r - leisure, l 0 l▯ h 4. The four conditions that a competitive equilibrium must satisfy are (a) The representative consumer chooses C and N to maximize utility, U, taking
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