A firm's production function is Q = K (L + 1), where L is hours of labor hired and K is K and MPK = L+ 1. The $10 per hour. (Round hours of capital hired. For this production function, MPL $5 per hour and the rental rate of capital is r = price of labor is w = answers to two decimals if necessary.) Assuming an interior solution, the long run demand for labor is L = (This may be a function of Q) Assuming an interior solution, the long run demand for capital is K = (This may be a function of Q.) Suppose the firm needs to produce Q = 50 units, then their long run total cost is $

A firm's production function is Q = K (L + 1), where L is hours of labor hired and K is K and MPK = L+ 1. The $10 per hour. (Round hours of capital hired. For this production function, MPL $5 per hour and the rental rate of capital is r = price of labor is w = answers to two decimals if necessary.) Assuming an interior solution, the long run demand for labor is L = (This may be a function of Q) Assuming an interior solution, the long run demand for capital is K = (This may be a function of Q.) Suppose the firm needs to produce Q = 50 units, then their long run total cost is $

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.7P

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Consider the following shortrun production function: Q =100L - L2 where Q is the output level and L is labour input. If the price of output in the market is K.sh 50 and labour costs K.sh 1200 per hour, how many hours would the firm use to maximize profits. What is the profit maximizing level of output?
Roland Umbrellas has a production function given by Q = L0.5K0.5. The wage (W) is $80 per day and the rental per unit of capital (R) is $5 per day. In the long run, how many units of capital will Roland want to buy for each unit of labor?
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Suppose that John is a shrubber. As a master shrubber, he hires apprentices, L, at wage w and purchases capital, K, (electric shrubbery trimmers, for example) to create his high-end shrubberies. Capital is expensive, so he generally borrows money to purchase the equipment. The cost of capital is r. John can produce shrubberies according to the production function q = 10 · K^1/4 L^1/4. We can assume John is a price taker. If wages are $10/hour, the cost of capital is $40/hour, and shrubberies sell for p = $160, how many shrubberies will John produce and sell? How much labor and capital will he purchase to produce that output? What are his profits?
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