oj Consider the Cobb-Douglas production function P(L, K) total units of production when 19 units of labor and 12 units of capital are invested. 6L0.6 K0.4. Find the %3D
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- A firm estimates its cubic production function of the form Q = AL^3 + BL^2 and obtains the following estimation results: A. What are the estimated total, average, and marginal product functions? B. At what level of labor usage is average product at its maximum?A second firm's production function is given by the equation Q = 12L.5K.5. Input prices are $36 per labor unit and $16 per capital unit, and P = $10. a. In the short run, the firm has a fixed amount of capital, K = 9. Create a spreadsheet to model this production setting. Determine the firm's profit - maximizing employment of labor. Use the spreadsheet to probe the solution using your spreadsheet's optimizer.Suppose a Cobb-Douglas Production function is given by the function: P(L,K)=8L^0.7K^0.3Furthemore, the cost function for a facility is given by the function:C(L,K)=300L+500KSuppose the monthly production goal of this facility is to produce 20,000 items. In this problem, we will assume LL represents units of labor invested and KK represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs?Units of Labor LL = (Show your answer is exactly 1 decimal place)Units of Capital KK = Incorrect (Show your answer is exactly 1 decimal place)Also, what is the minimal cost to produce 20,000 units? (Use your rounded values for LL and KK from above to answer this question.)The minimal cost to produce 20,000 units is $ Hint: Your constraint equation involves the Cobb Douglas Production function, not the Cost function. When finding a relationship between LL and KK in your system of…
- Margeʹs Hair Salon production function is Q = f(K, L) = K0.5L0.5 where K is the number of hair dryers and L is the number of labour hours she employs. 1. Prove, with the aid of mathematics, the type of returns to scale exhibited by this production function.Q)solve it correctly The marginal products of capital (MPK) and labor (MPL) are, respectively, MPK = 2000 units; MPL = 1500 units. The input prices are: PK = $10/unit; and PL = $150/unit. To minimize production costs, the firm should A. increase both capital and labor B. decrease both capital and labor C. increase capital; decrease labor D. decrease capital; increase labor E. do nothing; costs are minimizedThe engineers at Morris Industries obtained the following estimate of the firm’s production function Q = F ( K, L ) = min { 3K, 4L } How much output is produced when 2 units of labor and 5 units of capital are employed?
- You are a manager at Glass Incorporated—a mirror and window supplier. Recently, you conducted a study of the production process for your single-side encapsulated window. The results from the study are summarized in the following table and are based on the 8 units of capital currently available at your plant. Each unit of labor costs RM 60, each unit of capital is RM 20, and your encapsulated windows sell for RM 12 each. Labor L Capital K Output Q Marginal Product of Labor MPL Average Product of Labor APL Average Product of Capital APK Value Marginal Product of Labor VMPL 0 8 0 1 8 10 2 8 30 3 8 60 4 8 80 5 8 90 6 8 95 7 8 95 8 8 90 9 8 80 10 8 60 11 8 30…You are a manager at Glass Incorporated—a mirror and window supplier. Recently, you conducted a study of the production process for your single-side encapsulated window. The results from the study are summarized in the following table and are based on the 8 units of capital currently available at your plant. Each unit of labor costs RM 60, each unit of capital is RM 20, and your encapsulated windows sell for RM 12 each. Labor L Capital K Output Q Marginal Product of Labor MPL Average Product of Labor APL Average Product of Capital APK Value Marginal Product of Labor VMPL 0 8 0 1 8 10 2 8 30 3 8 60 4 8 80 5 8 90 6 8 95 7 8 95 8 8 90 9 8 80 10 8 60 11 8 30…The production function is f (L, M) = 5L1/2M1/2, where L is the number of units of labor and M is the number of machines. If the amounts of both factors can be varied and if the cost of labor is $9 per unit and the cost of using machines is $64 per machine, then the total cost of producing 12 units of output is a. $438. b. $108. c. $576. d. $115.20. e. $57.60.
- The production function q = K1.2 + 3L1.2 exhibits [increasing return to scale, constant return to scale, decreasing constant return to scale]The production function is f (L, M ) = 5L1/2M 1/2, where L is the number of units of labor and M is the number of machines. If the amounts of both factors can be varied and if the cost of labor is $9 per unit and the cost of using machines is $64 per machine, then what is the total cost of producing 12 units of output?For the production function Q = 0.2L2 returns to scale is: a.Constant Returns to Scale b.Decreasing Returns to Scale c.Increasing Returns to Scale d.Zero Return to Scale
