Question

You are the manager of Colgate, and the demand and cost functions for Colgate the enamel toothpaste are given by Q = 48-2P and C(Q) = 100 – 8Q + Q².

1. 1. Find the inverse demand function for Colgate toothpaste.
2. 2. Find the price and output that maximize profits.
3. 3. Compute Colgate profits.
4. 4. Given the answer to question 3, explain what would happen in the industry and to the firm in the long-run.

Answer 1

Inverse demand function P = 48/2 – Q/2 or P = 24 – 0.5Q. Marginal revenue is twice the slope MR = 24 – Q. Marginal cost MC = 2Q – 8. At the profit maximizing level of output, MR = MC which gives

24 – Q = 2Q – 8

32 = 3Q

Quantity Q = 10.7

Price = 24 – 0.5*10.7 = 18.7

Profits = PQ – C = 18.7*10.7 – 100 + 8*10.7 – 10.7^2 = 71.

In the long run, there is an expectation that new firms will enter attracted by short run profits. This would reduce the demand for Colgate and its price will reduce eliminating all the profits. Hence in the long run it would earn only accounting profits.