John provides cheese (H)and milk (M)to the market with the following total cost function C(H,M)= 8 + 0.5H² + 0.1M².The prices of cheese and milk in the market are $3 and $4 respectively.Assume that the cheese and milk markets are perfectly competitive.What output of milk maximizes profits?

Question

Quizplus · Accepted Answer

To find the output of milk that maximizes profits, we need to use the profit maximization rule in a perfectly competitive market, which is to produce at the output level where Marginal Revenue (MR) equals Marginal Cost (MC).

First, we need to calculate the Total Cost (TC) function by plugging in the given prices for cheese and milk into the total cost function:

C(H,M) = 8 + 0.5(3)H + 0.1(4)M
TC = 8 + 1.5H + 0.4M

Next, we need to find the Marginal Cost of producing milk (MC_M). Taking the derivative of the TC function with respect to Milk (M), we get:

MC_M = 0.4

Now, we need to find the Marginal Revenue (MR) of selling milk. In a perfectly competitive market, the price of the good equals the Marginal Revenue, so:

MR_M = 4

To find the profit-maximizing output of milk, we set MR_M equal to MC_M and solve for M:

MR_M = MC_M
4 = 0.4
M = 20

Therefore, the output of milk that maximizes profit is 20. We do not need to consider the output level of cheese, as the problem only asks for the optimal output of milk.

John Provides Cheese (H)and Milk (M)to the Market with the Following