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A manufacturing firm's production function is Q = KL + K + L. The price r of capital services is equal to 1, and let w denote the price of labor services. If the firm is required to produce 5 units of output, for what values of w would a cost-minimizing firm use

a) only labor?

b) only capital?

c) both labor and capital?

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Ronald
RonaldLv2
28 Sep 2019
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Related questions

Ben and Geri have changed their production methods and are now producing ice cream according to the production function,

Y=KL,

1. The price of a machine is R= 2 dollars and a laborer costs W= 1 dollar, the expenditure level E=$8, Determine the slope of the iso-expenditure curve

2. By setting the MRTS equal to the slope of the iso-expenditure curve, determine the mascot-minimizing capital-labor ratio (K/L) with R=2 and W=1. Given that the firm wants to produce Y=8 units of output, what is the optimal level of capita and labor for the firm? what is the cost-minimizing level of expenditure E when the firm produces Y=8 pints of ice cream?

3.Suppose the price of a laborer goes up to W=2. What are the new cost-minimizing levels of capital and labor given that Ben and Geri are still producing Y=8 pints of ice cream? What is the new cost-minimizing level of expenditure

Consider the following production function

q= f(k,l)= kl, where k is capital and l is labor used. Assume the k is fixed at 2 units. Rental rate of capital is given by r and wage rate of labor is given by w.

a) Are we in long run or short run? Why?

b) Find the Cost function for this firm.

A firm produces according to the following production function: Q = K^.5L^.5 where Q = units of output, K = units of capital, and L = units of labor. Suppose that in the short run K = 100. Moreover, the wage of labor is W = 5 and the price of the product is P = 10. What are the optimal units of labor?

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