Part II: work (including formulas or conditions invoked) and sketching diagrams

Question

Part II: work (including formulas or conditions invoked) and sketching diagrams as requested. Be certain to indicate which question you are answering and write on only one side of each page in the bluebook ysis Questions. Select three of the following four questions to answer, showing your 2 9) Suppose that the market demand function of a perfectly competitive industry is given by 0 4500 - 50P and the market supply function is given by Q-1550+50P where Q is in hundreds of units. a) Find the equilibrium price and quantity. b) Consider an individual firm in this perfectly competitive industry with MC = 10 + 2Q, what is the profit maximizing quantity of output? c) Assuming the firm in part b is representative of the other firms in the industry, approximately how many firms are operating in the industry? 10) Given a single price monopolist faci a) What is the total revenue at 0-6 units? b) What is the value of consumer surplus at 0-6 units? c) What is the total revenue at the profit-maximizing P and Q? d) What is the value of consumer surplus at the profit-maximizing P and Q? 11) Sketch a single-price monopolist with upward sloping marginal cost. a) Identify the profit-maximizing price and quantity; label them Pm and Qm, respectively. b) Now, impose the perfectly competitive outcome on the monopolist and identify the equil price and quantity, labeling them Ppc and Qpe, respectively c) Shade the area corresponding to deadweight loss associated with a monopoly d) Now assume the monopolist practices first degree or perfect price discrimination; ider 0 quantity and price. What happens to the deadweight loss identified in part c

Explanation / Answer

9 a) Market Demand,Q=4500-50P

Market Supply,Q=1550+50P

Market is in equilibrium where Demand equals supply.

Hence,

4500-50P=1550+50P

solving this gives P=29.5

Put P=29.5 in either the Market demand function or the market supply function to obatin the equilibrium quantity. Q=4500-50x29.5

=3025

Since Q is in hundreds of units, equilibrium Q=302500

b) MC for an individual firm is 10+2Q

We know that in a perfectly competitive market a firm will produce where P=MC

Hence , 29.5= 10+2Q

Solving this gives Q=9.75

Profit maximising output for an individual firm is thus 975 units of output. (9.75x100)

c) Let there be n number of firms in the industry.

Hence, 302500=nx 975

this gives n=310.25,that is 310.

There are 310 firms in the industry.

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