Consider the one-period economy discussed in class. The consumer maximizes a well- behaved utility function U(C, 1) subject to the budget constraint and where leisure is such that l = h - N. Capital is fixed. Firms choose labour to maximise profits subject to the technological constraint Y = zF(K, Nd), where F(K, Nd) is well behaved. Moreover, suppose that to finance the government spending G, the government imposes a tax on firm labour 7 and acquires a lump-sum tax T from the consumer. That is, the firm pays Tw units of consumption goods to the government for each unit of labour and the consumer pays T units of consumption goods. There are no other tax instruments. (a) (10 points) Write down the firm's problem and its first order condition. (b) (15 points) Study the effect of the introduction of the tax on firm labour and provide an economic interpretation. Hint: to study this effect plot the labour demand curves when 7 = 0 and when T > 0 (c) (10 points) Define a competitive equilibrium of this macroeconomy. (d) (10 points) List the full set of conditions characterising the competitive equilib- rium given the exogenous variables. (e) (10 points) Show that the Walras' law holds. Given your answer on point (c), explain how we can determine the endogenous variables in this model. (f) (15 points) Suppose that the government wants to choose 7 and T in order to reach the Pareto optimum in the market equilibrium. How should the government set 7 and T? Explain your answer.
Consider the one-period economy discussed in class. The consumer maximizes a well- behaved utility function U(C, 1) subject to the budget constraint and where leisure is such that l = h - N. Capital is fixed. Firms choose labour to maximise profits subject to the technological constraint Y = zF(K, Nd), where F(K, Nd) is well behaved. Moreover, suppose that to finance the government spending G, the government imposes a tax on firm labour 7 and acquires a lump-sum tax T from the consumer. That is, the firm pays Tw units of consumption goods to the government for each unit of labour and the consumer pays T units of consumption goods. There are no other tax instruments. (a) (10 points) Write down the firm's problem and its first order condition. (b) (15 points) Study the effect of the introduction of the tax on firm labour and provide an economic interpretation. Hint: to study this effect plot the labour demand curves when 7 = 0 and when T > 0 (c) (10 points) Define a competitive equilibrium of this macroeconomy. (d) (10 points) List the full set of conditions characterising the competitive equilib- rium given the exogenous variables. (e) (10 points) Show that the Walras' law holds. Given your answer on point (c), explain how we can determine the endogenous variables in this model. (f) (15 points) Suppose that the government wants to choose 7 and T in order to reach the Pareto optimum in the market equilibrium. How should the government set 7 and T? Explain your answer.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Consider the one-period economy discussed in class. The consumer maximizes a well-
behaved utility function U(C, 1) subject to the budget constraint and where leisure is
such that l = h - N. Capital is fixed. Firms choose labour to maximise profits subject
to the technological constraint Y = zF(K, Nd), where F(K, Nd) is well behaved.
Moreover, suppose that to finance the government spending G, the government imposes
a tax on firm labour 7 and acquires a lump-sum tax T from the consumer. That is, the
firm pays Tw units of consumption goods to the government for each unit of labour and
the consumer pays T units of consumption goods. There are no other tax instruments.
(a) (10 points) Write down the firm's problem and its first order condition.
(b) (15 points) Study the effect of the introduction of the tax on firm labour and
provide an economic interpretation. Hint: to study this effect plot the labour
demand curves when 7 = 0 and when T > 0
(c) (10 points) Define a competitive equilibrium of this macroeconomy.
(d) (10 points) List the full set of conditions characterising the competitive equilib-
rium given the exogenous variables.
(e) (10 points) Show that the Walras' law holds. Given your answer on point (c),
explain how we can determine the endogenous variables in this model.
(f) (15 points) Suppose that the government wants to choose 7 and T in order to
reach the Pareto optimum in the market equilibrium. How should the government
set 7 and T? Explain your answer.
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