In country V, the government is the monopolist that produces all iron. The market demand for iron is

Q_d = 10,000 – (2/5)P

The Total Cost of the monopolist is: TC = 5/2 Q^2

a. Write down the inverse demand function. Find the Average Total Cost (ATC) function

b. What does the monopolist control to maximize its profit?

c. Write down the profit as a function of quantity.

d. Find the Marginal Cost and Marginal Revenue functions

e. Find the optimal quantity of output for the monopolist

f. Find the Price that the monopolist charges, assuming no price discrimination

g. What is the monopolist’s profit?

h. Present the Demand curve, MR curve, MC, ATC, and Profit in a graph

i. Calculate the consumer surplus, producer surplus, and deadweight loss in the monopoly market.

j. Assuming the market demand and supply stays the same, but the market is perfectly competitive. Calculate consumer surplus and producer surplus for this perfectly competitive market.

k. Compare CS and PS in part (i) and part (j).