A monopolist produces two goods as follows: p= 11-0.5x, q = 51- 0.5y where p and q are prices per unit of the two goods, and x and y are the corresponding quantities. The cost function is given by C(x,y) = x+y 1. Derive the firm's total profit function. 2. Find the values of x and y that maximize profit. 3. Verify that you have found the maximum profit. 4. Suppose that the firm is required to produce a total of 60 units only. Find the values of x and y that maximize profits.
A monopolist produces two goods as follows: p= 11-0.5x, q = 51- 0.5y where p and q are prices per unit of the two goods, and x and y are the corresponding quantities. The cost function is given by C(x,y) = x+y 1. Derive the firm's total profit function. 2. Find the values of x and y that maximize profit. 3. Verify that you have found the maximum profit. 4. Suppose that the firm is required to produce a total of 60 units only. Find the values of x and y that maximize profits.
Chapter14: Monopoly
Section: Chapter Questions
Problem 14.5P
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Transcribed Image Text:A monopolist produces two goods as follows:
p= 11-0.5x,
q= 51-0.5y
where p and q are prices per unit of the two goods, and x and y are the corresponding quantities.
The cost function is given by
C(x,y) = x+y
1. Derive the firm's total profit function.
2. Find the values of x and y that maximize profit.
3. Verify that you have found the maximum profit.
4. Suppose that the firm is required to produce a total of 60 units only. Find the values of x and y that
maximize profits.
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