Question

# 1). The market demand function for a good is given by Q = D(p) = 800...

1). The market demand function for a good is given by Q = D(p) = 800 − 50p. For each firm that produces the good the total cost function is TC(Q) = 4Q+( Q2/2) . Recall that this means that the marginal cost is MC(Q) = 4 + Q. Assume that firms are price takers.

(a) What is the efficient scale of production and the minimum of average cost for each firm?

Hint: Graph the average cost curve first.

(b) What is the supply function of each firm?

(c) If there are currently 100 firms producing the good, what is the market supply function? What is the short-run competitive equilibrium in this market with 100 firms? What is the profit of each firm?

(d) What is the long-run competitive equilibrium price and quantity in this market?

2). Consider the market of the previous question in the short run (with 100 firms), and assume that the government imposes a tax of \$3 per unit.

(a) What would be the new equilibrium quantity supplied after the tax is imposed?

(b) What would be the price consumers pay and the price sellers receive with the tax? Explain how the burden of the tax is shared between consumers and producers.

(c) Compute consumer and producer surplus before and after the tax. How much government revenue is generated by the tax? How large is the deadweight loss?

(d) What would be the long-run equilibrium quantity in this market with the tax? What are the prices that consumers pay and sellers receive? Compare this to the long-run equilibrium without the tax and determine how much of the burden of the tax is borne by consumers and producers.

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