t Bob’s Burgers, each burger consists of exactly two buns x, one meat patty y, and one slice of cheese z. Let P denote the price of burgers and px, py, pz be the prices of each input and consider Bob’s profit maximization problem. (a) Write Bob’s production function q = f(x, y, z), show that it exhibits constant returns to scale, and find the marginal products to each factor. (b) Set up Bob’s cost minimization problem, write the Lagrangian L, and show why you cannot use the first order conditions to solve it. (c) (10) Solve for Bob’s cost function C(q), and find the average cost A

Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter21: Production And Costs
Section: Chapter Questions
Problem 17QP
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At Bob’s Burgers, each burger consists of exactly two buns x, one meat patty y, and one slice of cheese z. Let P denote the price of burgers and px, py, pz be the prices of each input and consider Bob’s profit maximization problem.


(a) Write Bob’s production function q = f(x, y, z), show that it exhibits constant returns to scale, and find the marginal products to each factor.


(b) Set up Bob’s cost minimization problem, write the Lagrangian L, and show why you cannot use the first order conditions to solve it.


(c) (10) Solve for Bob’s cost function C(q), and find the average cost AC(q) and marginal cost MC(q) functions.

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