LABOR ECONOMICS
8th Edition
ISBN: 9781260004724
Author: BORJAS
Publisher: RENT MCG
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Chapter 3, Problem 1P
To determine
Find the combination of input and the
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- Given the production function y= f(x1,x2)=x11/3x21/3. The amount of x2 is equal to 216 in the short run. Calculate the factor demand function Given the product price (P) is 6 and the price of factor 1 (w1) is 12, calculate the optimum amount of factor 1. Show your results on a graph.arrow_forwardSuppose that the production of a certain product only requires one input, labor, and that the additional production diminishes by half after the last input. On the other hand, the demand of the good can be described using the equation Q = 10000 – P/10. The total product of the second unit of labor is 3,000 unite. Finally, each additional worker requires P1,000,000. Given the following information, answer the following questions: What is the marginal revenue product of the third unit of labor? Answer: 500 How would you characterize the marginal revenue product of labor? How would you characterize the labor market that this firm faces?arrow_forwardSuppose that a firm’s production function is q =L0.5K0.5. This means that the marginal rate of technical substitution is K/L.The cost of a unit of labour is $20 and the cost of a unit of capital is $80. The firm wants to produce 50 units of output. If both capital and labour are variable, how many units of labour (L) and how many units of capital (K) should be hired in the long run? A. K = 25, L =100 B. K = 10, L = 100 C. K = 25, L =10 D. K = 7, L = 28arrow_forward
- A firm has a production function of Q = KL + L, where MPL = K + 1 and MPK = L. The wage rate (W) is $100 per worker and the rental (R) is $100 per unit of capital. The firm is producing 100 units of output. In the long run, what is the firm's Marginal Rate of Technical Substitution?arrow_forwardSuppose that a firm's estimated production is: Q = K³/411/4 What is the marginal rate of technical substitution (MRTS) equal to?arrow_forwardConsider the following production function: Currently the wage rate (w) is $5.00 and the price of capital (r) is $5.00. If the firm is using 20 units of capital in production, how much labor should be employed to minimize costs? Labor input = units. (Enter a numeric response using a real number rounded to two decimal places.) q=100L0.80.4arrow_forward
- Assume a firm is trying to produce q0 units of output at the lowest total cost. The wage decreases, rotating the isocost line as shown in the below graph. Make the necessary changes to the graph to show the input combination that will now produce q0 at the lowest total cost. Make sure you show the new levels of labor and capital.arrow_forwardA firm produces output according to the production function Q = 4K + 8L where K is capital and L is labour. If the wage rate is €60 and the cost of capital is €20, how many units of capital should the firm hire if it wants to produce 16 units of output? 4 2 0 08arrow_forwardConsider a firm that employs capital (K) and labour (L) and uses the production technology Q = 3K + 4L. Let factor prices be r = $40 for capital and w = $20 for labour. a) What is the firm’s minimization problem? b) Plot the isoquant for Q =100. What is the Marginal Rate of Technical Substitution (MRTS)? c) For any output Q, what is the optimal combination of K and L given the input prices? Hint set MRTS = r/w and solve for L) d) What is the cost function? Confirm C(Q=100) = 500 e) Given the above, what must the supply curve look like in long-run equilibrium?arrow_forward
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