1.Profit Maximization - Competitive Markets and Monopoly (20 points in total)

Consider the following demand- and supply curves for the widget industry in the short-run:

Q^d = 80 P ;Q^s = 20 + 4P

In the equations above Q^d and Q^s denotes market demand and -supply of widgets, respectively, and P denotes the market price for widgets.

(a)Determine the equilibrium output and price of widgets. (2 points)

A firm active on the market for widgets has the following total cost (C) and marginal cost (MC) functions:

C = 36 + q²;MC = 2q

In the equations above q refers to the output of widgets of an individual firm.

(b)What is the profit maximizing output of that widget producer? How many producers areactive on the widget market if all firms are identical? Do you expect more firms to enter the market over time?Why?What will happen to the market price of widgets in the long-run?(6 points)

(c)In the long-run, derive lowest price possible on the widget market that would allow your widget firm to stay in business? How large are the economic profits the firm runs at thisprice? (4 points)

Over time all but one widget producer disappear from the market, suchthatthewhole market demand of widgets is satisfied by the remaining firm only.

(d)What is the profit-maximization rule for this monopolist? Calculate the profit-maximizing output of this monopolist and its profits. (6 Points)

Hint: You might want to reformulate the market demand curve as: P = 80 Q.

(e)Draw the supply-curve of the monopolist. (2 Points)