Problem 1 The production function for a product is given by Q = 100KL. The price of capital is $120 per day and the price of labor $30 per day. What is the rate MPL/MPK for this production formula? Derive the optimal labor L∗ and optimal capital K∗ as functions of Q. Write down the Total Cost What is the minimum cost of producing 1000 units of output?

Problem 1 The production function for a product is given by Q = 100KL. The price of capital is $120 per day and the price of labor $30 per day. What is the rate MPL/MPK for this production formula? Derive the optimal labor L∗ and optimal capital K∗ as functions of Q. Write down the Total Cost What is the minimum cost of producing 1000 units of output?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Hi, please help with the question
A firm’s production is represented by the following function: Q = L1/4 K3/4 . The rental rate of capital (r) is $40 and the wage rate (w) is $12.a. For a given level of output, what should be the ratio of capital to labor in order to minimize costs?b. How much capital and labor should be used to produce 400 units of output? What is the total cost?c. What is the short run total cost if output is decreased to 300 units?d. How would the capital labor choice and total cost change in the long run?e. Would the firm prefer to relocate if input prices are r = 60 and w = 8 at an alternativelocation assuming relocation is costless?
Solve the attahment.
Consider the following marginal cost function MC= 5 + 2qi. (a) Does the production process exhibits increasing returns? decreasing returns? constant returns? (b) If the price is $23. What’s the optimal production level? (c) If the price is $31. What’s the optimal production level?
Please help solve for (b) what is long run cost in a?