The production function for Q is given as Q = 5K1/2L1/2where K is the amount of capital employed and L is the amount of labor employed. The price of capital is $8 and the price of labor is $4. Show the input choice when output reaches 59 and find the marginal cost of the 60th unit of output. Show your steps of calculation clearly.

The production function for Q is given as Q = 5K1/2L1/2where K is the amount of capital employed and L is the amount of labor employed. The price of capital is $8 and the price of labor is $4. Show the input choice when output reaches 59 and find the marginal cost of the 60th unit of output. Show your steps of calculation clearly.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.7P

See similar textbooks

Similar questions

What is the difference between a fixed input and a variable input?
You are running a small factory that uses labour (L) and capital (K) to produce output (Q). Your production function is Q space equals space 10 L to the power of bevelled 1 half end exponent K to the power of bevelled 1 half end exponent For every unit of labour you use you have to pay a wage of w = $ 20 and for every unit of capital you use you have to pay a rental rate of r = $5. You've signed a contract that you will produce Q = 700 units of output. If you minimize your costs, what amount of labour (L*) should you use?
Suppose that a firm's production function is Q = F(L) = -1L³-30L² + 5,000L. Its marginal product of labor is MPL = -3L2-60L +5,000. a. At what amount of labor input are the firm's average and marginal product of labor equal (other than at L = 0)? Instructions: Enter your answer as a whole number. units. b. Confirm that the average and marginal product curves satisfy the relationship discussed in the text. When the amount of labor input is less than the quantity identified in your answer above, the marginal product of labor is greater than the average product of labor. When labor is greater than the amount identified above, the marginal product of labor is less than the average product of labor.
Exercise 11 Question Help Suppose that a firm's production function is: 112- q = 10L0.5K0.5 98- Its marginal product functions are: 84- MP, = 5KO.5/L0.5 - 0.5g/L 70- and MPK = 5L0.5/K.5 - 0.5g/K. 56- The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. 42- 28- Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. 14- -q= 280 q= 140 98 Suppose now that the firm wants to increase output to 280 units. If capital is fixed 0- in the short run, how much labor will the firm require? 70 84 L, Units of labor 14 28 42 56 112 The firm will now require units of labor. (Enter your response rounded to two decimal places.) K, Units of capital
Consider the production function Y AK°Lta, where A is a constant, L is labour, K is capital and a 0. Which of the following is true? O The marginal product of labour is constant O The marginal product of labour is diminishing There are increasing returns to scale O There are decreasing returns to scale
Suppose that firm's short-run 4 a production function is q=10/T – 1. 5.1 Find the level(s) of maximise the firm's average product of L that labour (APL). 5.2 Calculate the value of the second- order derivative (SOD) at the value of L found in 5.1 that maximises APL 5.3 Calculate the marginal product of labour (MPL) at the level(s) of L that maximises APL
Consider the production function of the firm below. Which of the following is NOT true? The marginal product of labor at B is 70 units. The total product is increasing as inputs to production increase. The marginal product of capital at point D is 50. The marginal products of both labor and capital are always increasing.
1. For each of the following production functions, (a) F(L, K) = LK³ (b) F(L, K) = L+3K (c) F(L, K) = (min{L, K})³ i. Sketch a representative isoquant. ii. Calculate the marginal product for each input, and indicate whether each marginal product is diminishing, constant, or increasing. iii. Calculate the marginal rate of technical substitution for each function. iv. Also indicate whether the function exhibits constant, increasing, or diminishing returns to scale.
A production function is represented by P=f(L), where L is labour. As input L increases, the total output will increase but what will happen to marginal product? Can marginal product be zero? if so, what it mean
A firm's production function is q = min (0.5K, 5L).The current wage rate, w = $10 and the price of capital, r= $5. How many units of K and Lshould the firm hire in order to produce 180 units of output with the minimum cost?Please find the solution and also draw the isoquant and the isocost curve
12
The marginal product of labor can be determined using the total product of labor curve. Using the equation for the production function, the level of output when L = 8 and K = 25 is (3) 2³. (Enter a numeric response using a real number rounded to two decimal places). q=8LK+5L² Product or Output (q) 3,500- 3,000- 2,500- 2,000- 1,500- 1,000- 500- 0- Production Function 5 2 :8 15 15 10 Labor Input (L) 20 25