Microeconomic question from Sejong University student.

1. Suppose there is only one firm in the market. The market demand curve is P(Q)=30-Q. The cost of production is C(Q)=10+0.5Q^2.

(a) Derive a firm's marginal cost.

Suppose the firm is a price taker.

(b) What is the firm's marginal revenue?

(c) Derive a firm's supply curve.

(d) Draw the supply and demand curves. Find the equilibrium price and quantity.

Now suppose the firm is a monopolist in the market.

(e) What is the firm's marginal revenue?

(f) Derive the monopolist's profit-maximizing quantity supplied and the price of the good.

(g) Compute the price elasticity of demand at the price set by the monopolist and make sure a monopolist's pricing rule (a rule of thumb for pricing) holds.

(h) Compare (d) and (f) and explain why you have such a result.