Suppose that the production function takes the form Q=L-0.7L^2. In addition, marginal revenue is $10 and marginal cost is $1. The optimal number of hours of labor is ___.
Suppose that the production function takes the form Q=L-0.7L^2. In addition, marginal revenue is $10 and...
6. Suppose the production function takes on the following form: Q=K’L? a) What is the marginal productivity of labor? Evaluate it at L = 5 and K = 7. (5 points) b) What is the Marginal Rate of Technical Substitution? Evaluate it at L = 5 and K = 7. (5 points)
3. Suppose the production function takes on the following form: Q = aK2L 2 a) What is the marginal productivity of labor? Evaluate it at L = 2 and K = 4. b) What is the marginal productivity of capital? Evaluate it at L = 2 and K = 4. c) What is the Marginal Rate of Technical Substitution, and what does it mean? (Provide two interpretations of the MRTS) Evaluate the value of the MRTS at L = 2...
Suppose we have a production function Q = 16.7K - K^2. If marginal revenue is $10, what is the marginal revenue product of capital when K=4. Hint: Round your answer to two decimal places.
The production function for widgets takes the following form: q = 4L + 6K a. What is the least cost combination of L and K that the firm should employ to produce 48 widgets when w = 2 and r = 4. b. Suppose the price of labor increases to w = 4 but the rental rate of capital is unchanged. If the firm still wants to produce 48 widgets at the lowest cost possible, should it alter its input...
The production function of the Auto parts firm is given by Q-5L-L, where Q is the units of output and L is the number of labor hours. Each output sells for 100 dollars per unit. The human resources manager estimates that the marginal cost of hiring an extra worker is 50 dollars. How many labor hours should this firm hire? Hint: MPL=5-2 L 1) 2) A frim's production function is given by Q(L)-6L, where Q measures output and L is...
Consider the following short-run production function (where L = variable input, Q = output): Q=6L−0.4L2 Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input (L) as it needs at $20 per unit. What is the marginal revenue product function (MRPL)? $20 $60−$8L $10 $6−$0.40L What is the marginal factor cost function (MFCLMFCL)? $6−$0.40L $60−$8L $10 $20 What is the optimal value of L, given that the...
Suppose the production function for automobiles is ? = ?? where Q is the quantity of automobiles produced per year, L is the quantity of labor (man-hours) and K is the quantity of capital (machine hours). a) What is the total product (number of automobiles) if the firm uses 25 man hours and 2 machine hours? b) Sketch the isoquant corresponding to a quantity of Q=50. c) What is the general equation for the isoquant corresponding to any level of...
2. Suppose that a firm’s production function is Q = 10 L½ K½ and the unit cost of labor is $20, capital is $80, and the product price is $12 per unit. The firm is currently producing 100 units of output and has determined that its cost minimizing quantities of labor and capital usage for this level of output is 20 and 5 respectively. The product price is $12 per unit. a. Determine the current total cost for 100 units,...
Suppose a firm has the following production function: Q = 2K L. The marginal product of capital is 2L, and the marginal product of labor is 2K. Assume that capital rents for $100 per unit per day, that labor can be hired for $200 per unit per day, and that the firm is minimizing costs. a. The firm will hire units of labor and - units of capital. b. What is the total cost of producing 60 units of output?...
Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL = ½ L-1/2K1/2and MPK = ½ L1/2K-1/2 a) Suppose the price of labor is w = 18, and the price of capital is r = 2. Derive the firm’s total cost function. b) What is the firm’s marginal cost? c) For this problem, you will sketch the graph of the firm’s isoquant for Q...