Cambrian Railways runs a daily container freight train between Cardiff and Birmingham. Its two major customers are British Steel and the Welsh Farming Co-operative. The demand for containers by each customer is given by the equations:
P1 = 500- 8Q1 for British Steel
P2 = 400-5Q2 for Welsh farming.
P; is the price charged by Cambrian per container, and Q; is the number of containers used by each customer.
Cambrian's total cost function is given by the equation:
TC = 10 000+20Q where Q is the number of containers per trip.
a) What are the necessary conditions for profitable price discrimination by Cambrian?
b) What profit maximizing rule will Cambrian use if setting prices as a discriminator?
c) Determine the profit maximizing quantity of freight service Cambrian will supply, show how this will be divided between steel and agriculture and find the prices charged in each market. Calculate Cambrian's total profit.
d) Assume that Cambrian is prevented by law from price discrimination. Determine Cambrian's price and output combination to maximize profit, and hence estimate the opportunity cost to Cambrian of the Anti-Price Discrimination law.
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