Question

In: Economics

Suppose there are two inputs in the production function, labor and capital, and these two inputs...

Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitutes. The existing technology permits 5 machines to do the work of 2 workers. So the production function is f(E, K) = 2K + 5E. The firm wants to produce q units of output, where q > 0 is some number. Suppose the price of capital is $10 per machine per hour. What combination of inputs will the firm use if the wage rate is $15 or $25 or $35 per hour?

Solutions

Expert Solution


Related Solutions

Suppose there are two inputs in the production function, labor and capital, and these two inputs...
Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitutes. The existing technology permits 3 machines to do the work of 2 worker. So F(E,K)=2K+3E. The firm wants to produce 60 units of output. Suppose the price of capital is $10 per machine per hour. What combination of inputs will the firm use if the wage rate is $10 or $15 or $20 per hour? What if the firm wants to...
Suppose there are two inputs in the production function, labor and capital, which are substitutes. The...
Suppose there are two inputs in the production function, labor and capital, which are substitutes. The current wage is $10 per hour and the current price of capital is $25 per hour. Given the following information on the marginal product of labor and the marginal product of capital, find the firm’s profit-maximizing input mix (i.e. number of workers and units of capital) in the long-run. Show your work and explain. L MPL K MPK 1 125 1 130 2 100...
Consider a production function of two inputs, labor and capital, given by Q = (√L +...
Consider a production function of two inputs, labor and capital, given by Q = (√L + √K)2. Let w = 2 and r = 1. The marginal products associated with this production function are as follows:MPL=(√L + √K)L-1/2MPK=(√L + √K)K-1/2 a) Suppose the firm is required to produce Q units of output. Show how the cost-minimizing quantity of labor depends on the quantity Q. Show how the cost-minimizing quantity of capital depends on the quantity Q. b) Find the equation...
a) The standard economic model of a production function where capital and labor are inputs into...
a) The standard economic model of a production function where capital and labor are inputs into production, with both earning a return according to their marginal contribution to the value of output b) The Marxian approach of production as a labor process, where the value added is distributed between the capitalist and the worker. What is the most important difference in conclusions drawn from the the two approaches to production?
Capital and labor are the only two inputs for the following production process. Capital is fixed...
Capital and labor are the only two inputs for the following production process. Capital is fixed at 4 units, which costs 50 dollars each unit per day. Workers can be hired for 100 each per day. Complete the following table and plot the marginal cost (MC), average total cost (ATC), average variable cost (AVC), average fixed cost (AFC) on the same graph. The quantity of labor input Total output per day AFC AVC ATC MC    0 0 1 100...
A firm produces a product with labor and capital as inputs. Its production function is described...
A firm produces a product with labor and capital as inputs. Its production function is described by Q(L,K) = L^1/2 K^1/2. Let w and r be the prices of labor and capital, respectively. a. Derive the firm’s long-run total cost and long-run marginal cost functions. b. Assume capital is fixed at 4 units in the short-run and derive the firm’s short-run total cost and short-run average variable cost functions.   c. Rewrite your short-run and long-run total cost functions (for the...
A firm uses two inputs in production: capital and labor. In the short run, the firm...
A firm uses two inputs in production: capital and labor. In the short run, the firm cannot adjust the amount of capital it is using, but it can adjust the size of its workforce. -- If the cost of renting capital increases, which of the following curves will be affected? (Check all answers that apply). -- Average variable cost Marginal cost Average fixed cost Average total cost 2 points    QUESTION 2 If the cost of hiring workers increases, which...
Assume a firm has 2 inputs in its production​ function, labor and​ capital, and can adjust...
Assume a firm has 2 inputs in its production​ function, labor and​ capital, and can adjust the amount of either one of these inputs in order to increase output. Assume the marginal product of a unit of capital is always twice as high as the marginal product of a unit of labor​ (this is true regardless of how much labor and how much capital the firm​ employs). If the firm wanted to expand​ output, would they ever do so by...
Suppose that production of widgets requires capital and labor. The production function is constant returns to...
Suppose that production of widgets requires capital and labor. The production function is constant returns to scale and capital investment is sunk. There are no other barrier to entry. Is the investment in sunk capital a barrier to entry? Explain. What will the market equilibrium be if there are many possible entrants?
Suppose that an economy has a Cobb-Douglas production function with three inputs. K is capital (the...
Suppose that an economy has a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among workers). Markets for output and factors of production are both competitive. The production function is Y = K^1/3*L^1/3*H^1/3 1. Prove that this technology shows constant returns to scale. 2. Solve the competitive firm’s profit maximization problem by deriving the first-order conditions. 3. An...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT