Question 2 Please show all calculations to get credit (12 points) Consider a mon

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Question 2 Please show all calculations to get credit (12 points) Consider a monopolist who sells watches has the following demand function p = 100-Q and cost function TC Q2. Compute the equilibrium price, quantity, profit and consumer surplus set by the monopolist if the monopolist charges a uniform price (i.e. same price for all quantity). Compute the same numbers if this a. ??? monopoly would be under perfect competition MTR-TC:TR pxq (B points (for monopoly) +3 points (for competition) 6 points) Suppose a profit-maximizing monopolist producing Q units of output faces the demand curve P- 20-Q. Its total cost when producing Q units of output is TC-24+Q2. The fixed cost is sunk, you need to compute the Marginal Cost Curve. If price discrimination is impossible, how large will the profit of the monopolist be? Suppose the firm can engage in two-part tariff price discrimination (i.e. a gate fee and then each quantity is sold at a uniform price). How large will the profit of the monopolist be after two-part tariff price discrimination? How much extra profit does the producer capture when it can engage in two-part tariff price discrimination instead of charging a uniform price? MR-:MC's ; ? (uniform price)-m- TC: TR : p q (after two-part tariff) Gate Fee + Revenue-cost (3 points for monopoly + 3 points for two-part tariff 6points b. ??? aTR aq arc

Explanation / Answer

A. P = 100 - Q

TR = PQ = 100Q - Q2

MR = 100 - 2Q

TC = Q2

MC = 2Q

Monopolist will maximize profit at MR equals to MC

100 - 2Q = 2Q

4Q = 100

Q* = 25 units

P* = 100 - Q = 100 - 25 = $ 75 per unit

Profit = TR - TC = 75×25 - 252 = $ 1250

Consumer Surplus = (1/2)×(100 - 75)×(25 -0) = $ 312.5

Perfect Competition Profit maximizes when P = MC

100 - Q = 2Q

3Q = 100

Q = 33.33 units

P = 100 - 33.33 = $ 66.67 per unit

Consumer Surplus = (1/2)×(100-66.67)×(33.33-0)

= $1110.9

B. P = 20 - Q

TR = 20Q - Q2

MR = 20 - 2Q

TC = 24 + Q2

MC = 2Q

No price discrimination then MR = MC

20 - 2Q = 2Q

4Q = 20

Q* = 5 units

P* = $15 per unit

Profit = 15×5 - (24+52) = 75 - 49 = $ 26

When monopolist implements two part tariff then he must charge gate fee equal to monopoly price and uniform price equal to MC(Since under perfect competition P=MC).

Price under perfect competition

P= MC

20 - Q = 2Q

3Q = 20

Q* = 6.67 units

Pp = 20 - 6.67 = $13

Gate fee = $ 15

Price = $ 13 per unit

Profit = 15 + 13×7 - (24+72)= 15+91 -49 = $57

Extra profit due to two part tariff = $31 (=$57-$26)

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