Q3. Please answer all the questions so that I can verify with my own, thank you
ID: 1131958 • Letter: Q
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Q3. Please answer all the questions so that I can verify with my own, thank you so much!
3. Reconsider the BMW problem from class. BMW is pricing like a monopolist in two markets, the US and Germany. The demand function for the US, DUs(p), and for Germany, Dc(p), are as follows The firm produces and sells their vehicles at a constant marginal cost of $4. That is (a) Suppose BMW can control the reseller market (think, US customers cannot buy German-sold cars and vice versa) and offers a different price to the two markets. For each market, calculate the price BMW will charge, the equilibrium quantity, and all components of the market surplus (b) After losing control of the resale market, BMW is forced to offer a single price across both markets Recalculate the price, quantity, and surplus for each market (c) How do the surpluses compare under market-specific and uniform pricing? Which principle(s) of efficiency help explain the difference and why:? (d) Now suppose SupremeTM has decided to enter the market and sell completely non-functional, but well-branded, SupremeTM cars. They have the same cost as BMW and face the same demand schedules in both the US and Germany. They can charge either a uniform price or pay a fee to implement a SupremeTM region lock system and price to specific markets. How much would Supreme be willing to pay for this system?Explanation / Answer
1) Since the firm operates as a monopoly in both the market, it will produce in each market at the point where the marginal cost is equal to the marginal revenue.
In the US market,
DUS = q = 50-2p or p = (50 - q)/2
Total revenue = pq = (50 - q)q/2 = 25q - q2/2
Marginal revenue = 25 - q
Therefore, setting MR = MC , we get, 25 - q = 4 or q = 21
p = (50 - 21) /2 = 14.5
Since, the firm has complete knowledge about the demand function while practising price discrimination, it charges the consumers at their willingness to pay. So, the consumer surplus is zero.
The producer surplus is given by ( p - MC)q = (14.5 - 4) 21 = 220.5.
In the German market,
q' = 200 - 3p or p = (200 - q')/3
TR = (200 q' - q'2)/3
MR = 200/3 - 2q'/3 = MC = 4 or 2q'/3 = 200/3 or q' = 100
p = 100/ 3 = 33.33
Again the consumer surplus is zero. Producer surplus is (33.33 - 4)100 = 2933 .
b) When BMW followsthe single pricing policy, the market demand will be the sum total of the demands in the two separate markets.
Therefore, Q= q + q' = 50 - 2p + 200 - 3p = 250 - 5 p or p = (250 - Q)/5
TR = 50 Q - Q2/5
MR = 50 - 2Q/5 = 4 or 46 = 2Q/5 or Q = 115
p = (250 - 115 )/5 = 27
So the price in both markets is 27
q(US) = 50 - (2*27) = 50 - 54 = -4
Therefore, no sales will be made in the US market at this price.
In the German market, q(Germany) = 200 - (27*3) = 119
In the case of US, both consumer and producer surplus is zero.
In Germany, Consumer surplus = (33.3 - 27) 119 = 750
Producer surplus = (27 - 4) 119 = 2737
c) Total surplus with price discrimination = Producer surplus in US + Producer surplus in Germany
= 220.5 + 2933 = 3153.5
Total surplus with uniform pricing = Consumer surplus+ producer surplus
= 750 + 2737 = 3487
Therefore, the total surplus is greater when the uniform pricing is used as compared to price discrimination. The principle of pareto efficiency explains the difference in the two surpluses as no individual can be made better off without making someone worse off in the case of perfect price discrimination. After, the uniform pricing is implemented, total consumer surplus rises but the total producer surplus decreases. Therefore, this redistribution between consumer and producer surplus causes the difference. The uniform pricing increases the overall welfare in the society.
d) In order to be able to practice price discrimination and hence be able to appropriate greater producer surplus, Supreme will pay upto the difference between the producer surplus by price discrimination and uniform pricing, that is, 2933 - 2737 = 196. So the amount paid will be less than or equal to 196.
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