An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 23-0.2x (for 0 ≤ x ≤ 115), the price function for cars sold in Europe is q = 11 -0.1y (for 0 ≤ y ≤ 110), and the price function for cars sold in Asia is r = 14 -0.1z (for 0 ≤z ≤ 140), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 27 + 9(x+y+z) thousand dollars. (a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.] P(x, y, z) = (b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and P₂ equal to zero and solve. Assuming that the maximum exists, it must occur at this point.] America Europe Asia cars cars cars

An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 23-0.2x (for 0 ≤ x ≤ 115), the price function for cars sold in Europe is q = 11 -0.1y (for 0 ≤ y ≤ 110), and the price function for cars sold in Asia is r = 14 -0.1z (for 0 ≤z ≤ 140), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 27 + 9(x+y+z) thousand dollars. (a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.] P(x, y, z) = (b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and P₂ equal to zero and solve. Assuming that the maximum exists, it must occur at this point.] America Europe Asia cars cars cars

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.4P

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