Happy Cows and Free Cows are two separate perfectly competitive dairy farms. The table above shows the respective firms' marginal cost at various production levels.
-Refer to the table above. Suppose the perfectly competitive market for dairy products had a 40 percent chance of a high price of $3.00 and a 60 percent chance of a low price of $2.00. However, both Happy Cows and Free Cows have revised their probabilities and now believe that the probability of a high price of $3.00 is 80 percent and the probability of a low price of $2.00 is 20 percent. If the managers of Free Cows want to maximize expected profit based on the new probabilities by how much will they change the quantity produced?

Question

Quizplus · Accepted Answer

To maximize expected profit, Free Cows should produce the quantity where their marginal cost equals the expected market price, which is the weighted average of the high and low prices based on the new probabilities.

Expected market price = (0.8)($3.00) + (0.2)($2.00) = $2.60

At a market price of $2.60, Free Cows' profit-maximizing quantity is where MC = $2.60. This occurs at a quantity of 70 units, where the marginal cost is $2.60.

Therefore, Free Cows should increase their production by 20 units (from their initial quantity of 50 units) to reach the profit-maximizing quantity of 70 units.

Happy Cows and Free Cows Are Two Separate Perfectly Competitive