The purpose of this exercise is to contrast the incidence of a commodity tax under different market structures. Consider an economy with identical households and identical firms. The representative household receives labor income for its labor supply l and profit income p for its ownership of the firm. The utility function of the household is U = 2

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The purpose of this exercise is to contrast the incidence of a commodity tax under different market structures. Consider an economy with identical households and identical firms. The representative household receives labor income for its labor supply l and profit income p for its ownership of the firm. The utility function of the household is U = 2 - . The firm produces one unit of final consumption good x with one unit of labor input. Labor is the nume´raire good: the price of labor is normalized to 1, and labor is the untaxed good. The producer price is p and the consumer price is q = p + t, where t > 0 is the (specific) commodity tax.

a. Describe the household’s optimization program treating profit income and the consumer prices in the budget constraint as fixed. Find the demand for good x as a function of consumer price q.

b. Calculate the elasticity of the slope of the inverse demand function.

c. Suppose that the firms act in unison like a monopolist. Find the supply of the monopoly as a function of t.

d. What is the equilibrium price charged by the monopolist? What is the producer price? What is the division of the tax burden between the producer and the consumer?

e. Suppose that the firms act independently maximizing their own profit-taking prices as given. What is the equilibrium producer price? What is the division of the tax burden between producer and consumer? Compare with the result in part d.

 

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