The Director of Jonat Enterprise hires labour (L) and rents capital equipment (K) in a competitive market to produce chocolate pellets. At the moment, the wage rate of labour is GH¢2 per hour and capital is rented at GH¢5 per hour. Also, the unit price of chocolate pellets is GH¢0.75 and total cost of production is GHe 1,000. Suppose the firm's production function (Q) follows a Cobb-Douglas specification given as: Q = 14K0.5 10.5 + 10 Page 3 of 4

The Director of Jonat Enterprise hires labour (L) and rents capital equipment (K) in a competitive market to produce chocolate pellets. At the moment, the wage rate of labour is GH¢2 per hour and capital is rented at GH¢5 per hour. Also, the unit price of chocolate pellets is GH¢0.75 and total cost of production is GHe 1,000. Suppose the firm's production function (Q) follows a Cobb-Douglas specification given as: Q = 14K0.5 10.5 + 10 Page 3 of 4

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm has the production function Q(K, L)=KxL, where Q is the hours of edited footage. The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units of output at the lowest possible cost.a) Find the marginal product of each input.b) Determine whether the production function exhibits diminishing marginal product to each input.c) Find the marginal rate of technical substitution(MRTSLK)d) How does MRTSLK change as more L, is used holding output constant.e) Find the least costly combination of labor and capital to produce 3000 units
Suppose a firm with a production function given by Q = K0.4L0.6 produces 100 units of output. The firm pays a wage of $20 per units and pays a rental rate of capital of $40 per unit. (Note: MPL = 0.6K0.4L-0.4 and MPK = 0.4K-0.6L0.6 ) What is the minimum cost of producing 100 units of output?
Assume there is a linear isoquant where the input combination K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL = $1 and PK = $1. What is the smallest total cost necessary to produce Q = 100? $20 $10 $50 $100
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.
Suppose that the production function for Hannah and Sam's home remodeling business is Q=f(L,K) Q=1040.2K0.3 Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $2,000 per week. a. What is the least-cost input combination for remodeling 100 square feet each week? Instructions: Round your answers to 2 decimal places. units of labor and units of capital. b. What is the total cost? Instructions: Round your answer to 2 decimal places.
A firm produces plastic bins using labor (measured in man-hours) and capital (measured in machine-hours), according to the production function Q = f(L,K) = LK, where Q is the number of plastic bins produced. Suppose that the cost of labor is $20 per worker-hour and the cost of capital is $10 per machine-hour. What is the cost minimizing input combination if the firm wants to produce 28,800 plastic bins? Hint: The marginal products are MP, = K and MPg = L.
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…
The production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and L is labor and q is output d) Now suppose w =30 and r = 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) e) Now suppose that the firm is in the short run and cannot vary the amount of capital. That is, it must use the same amount of capital as in part d). However, the firm wants to produce 1200 units of output. How much labor should it use to minimize its cost and what is the minimum cost of producing q =1200?
Assume there is a linear isoquant where the input combination K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL= $1 and PK = $1.What is the smallest total cost necessary to produce Q = 100?
In the short run, a firm which has production function f(L, M) = 4L1/2M1/2 must use 4 machines. If the cost of labor is £4 per unit and the cost of machines is £4 per unit, what is the short-run total cost of producing 48 units of output? Use Lagrange
Consider the following table illustrating the production function of gadgets. Furthermore, suppose the firm has fixed costs of $2,000/day and the wage rate is $250/day. What is the firm's variable cost of producing 2,600 gadgets? a $1,000 b $1,750 c $2,000 d none of the above
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.