5 föt the factors of production be labor and capital equipment. A competitive firm is facing the followinginput prices: the wage rate is wi = $8 per hour and the rental rate of capital is w2 = $16 per hour. Atthe current input mix the marginal product of labor is 24 and that of capital is 32. Should the firmchange its input mix? Why?

Cost is minimized where the right combination of labor and capital is used. following is the…

Answered: Let the factors of production be labor…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Assume a firm has the following short-run production function: q(L) = L+6L2-1/2L3 If this firm is going to maximize profits in the short-run by producing a strictly positive level of output (q>0), what is the lowest level of labor (L) they would employ? A.) Minimum L=?
Suppose the long-run production function for a competitive firm is f(x1,x2)= min {x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the x1-y and x2- y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? .d. Write down the formula and draw the graph of the average cost function, as a function of y. .e. Write down the formula and draw the graph of the marginal cost function, as a function of y.
The answer should be typed
1. Suppose the total-cost function for a firm is given by C = qw 1/4 3/4 a. Use Shephard's lemma to compute the (constant output) demand functions for each input, k and 1. b. Calculate the average cost and marginal cost. c. Describe the returns to scale for the underlying production function for q.
A firm operates in the short run with the production function Q = 10 K0.5 L 0.5, where Q is output, K is capital, and L is labor. The price of capital is $100 per unit, and the wage rate is $50 per unit of labor. How many units of capital and labor should the firm use to minimize its total cost while producing 400 units of output?
The short run production function of a competitive firm is given The short-run production function of a competitive firm is given by f (L) = 6L2/3, where L is the amount of labor it uses. (For those who do not know calculus—if total output is aLb, where a and b are constants, and where L is the amount of some factor of production, then the marginal product of L is given by the formula abLb−1.) The cost per unit of labor is w = 6 and the price per unit of output is p = 3. (a) Plot a few points on the graph of this firm’s production function and sketch the graph of the production function, using blue ink. Use black ink to draw the isoprofit line that passes through the point (0, 12), the isoprofit line that passes through (0, 8), and the isoprofit line that passes through the point (0, 4). What is the slope of each of the isoprofit lines? (b) How many units of labor will the firm hire? (c) Suppose that the wage of labor falls to 4, and the price of output…
Assume that the production function for competitive firm is given by F(L)=9L1/3, where L is the number of units of labour used in the production process. Suppose that the cost per unit of labor is $3 and the price of output is $9 per unit, how many units of labor will the firm hire?
3
A firm has the following Cobb-Douglas production function: q=(L^α)(K^1-α)0<α < 1 is a parameter. Suppose in the short run K = 1. The rental rate of a unit of K is $10, and the wage rate of a unit of L is $20.(a) Derive the marginal cost of the firm (expressed in terms of α and q).(b) Derive the average variable cost of the firm (expressed in terms of α and q).(c) Derive the cost function of the firm.
handwrite it out step by step
The table below presents the output and input levels: K L Q 2 2 1 100 2 2 200 2 3 250 2 4 270 Also assume that the per unit cost of capital is $10. Since the firm has two units of capital, the firm's total fixed cost is $20. Also assume that the cost of each unit of labor is $50. What is the marginal cost when four units of labor (L) are employed?
A firm's production function is given by Q = 2K2 L/2 Unit capital and labor costs are $4 and $9, respectively. a) What is the cost function for the firm? b) If the firm is contracted to provide 144 units of output, what is the firm's constraint? Constraint: b) Find the values of K and L which minimize total input costs under the production constraint. K = units L= units

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Let the factors of production be labor and capital equipment. A competitive firm is facing the input prices: the wage rate is wi = $8 per hour and the rental rate of capital is w, = $16 per