1) The Cobb-Douglas production function is y = it vary with: (a) y: (b) 22/21. with a > 0 and 3 > 0. Show that MP₁ = ay/2₁, MP₂ = By/22. What is the MRT S21? How does
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- 10)Given the production function f (L K) = L2 / 3. K1 / 3, where L is the working hours and K is the capital. assuming that the capital price is r = 4 euros and the price per hour of work is w = 27 euros and that all the factors of production are variable, what is the minimum cost of producing 10 units of product? Choose one: A) 260e B) 230e C) 240e D) 250e E) 270eSuppose 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…Output Y is produced according to Y = F(K, L), where K is the capital stock and Lis the number of workers. The production function F(K, L) has constant returns toscale and diminishing marginal returns to capital and labour individually. The levelof technology is assumed to be constant over time. Capital per worker is denotedby k = K/L and output per worker by y = Y/L, and the two are related according toy = f(k), where f(k) = F(k, 1) is the per-worker production function. Investment is equal to saving, which is a constant fraction s of income Y. Capitaldepreciates at rate δ and the number of workers grows at rate n. The change incapital per worker over time is ∆k = sf(k) − (δ + n)k. Consider a country that has reached its steady-state capital per worker. Then, inone year, the country suffers severe flooding that destroys part of its capital stock.Assume this is treated as a one-off event that is not expected to reoccur. explain what happens to incomeper worker in the short run and the…
- Suppose that the production function takes the form X = min(10L, 5K) and that a competitive firm faces a wage rate of £60 per week and a weekly capital rental of £32. (a) How much must the firm spend to produce 100 units of output, and what is the average cost of production when X = 100? (b) What is the incremental cost of producing the 101st unit of output? (c) What happens to the cost of producing 100 units of output if the wage rate and the rental cost of capital rise by 25 per cent each? What happens to the average and marginal cost? (d) What happens to the cost of producing 100 units of output if the wage rate increases by £1, or if the cost of capital increases by £1?The cost formula for a company can be modeled by C=1092+40x+0.1x2C=1092+40x+0.1x2 where xx represents the number of items made. A formula for the company's income is modeled with R=108x−0.9x2R=108x-0.9x2, where xx is the number of items sold. A company will break even when its costs equal its income. How many items must a company make and then sell to break even? Answer: (If there are multiple answers, separate the answers with a comma.)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.
- A firm produces output according to a production function: Q = F(K,L) = min {4K,8L}. a. How much output is produced when K = 2 and L = 3? 192 Numeric ResponseEdit Unavailable. 192 incorrect.unit(s) b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 8 units of output? Capital: 80 Numeric ResponseEdit Unavailable. 80 incorrect. Labor: 480 Numeric ResponseEdit Unavailable. 480 incorrect. c. How does your answer to part b change if the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour? multiple choice Capital and labor increase. It does not change. Capital increases and labor decreases. Incorrect Capital decreases and labor increases.production function 10Q = 1600L-4,800, where L is hired labour hours. If the wage rate that laborers receive is $10/hour, what is the cost function?The production function for a firm is: q=-0.6L3+18L2K+10L where q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is w = $100 and the rental rate is r = $800 per time period. a Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. b For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost , AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram. Hint: you will not be able to solve the total product curve for L as a function of output. So, instead construct a table, See the headings. Use this definition ΔTC/Δq…
- How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether α1 + α2 is larger than, smaller than, or equal to one?Assume labor (L) is the only variable input used in the production process, a firm’s production function is given by Q=7L+10L2-L3 where Q represents total product. Classify the production function in to the three stages of production.Qno1.You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled Required. a). Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively at the Karachi plant. What will be your advice if workers’ marginal product is 40 at wage of Rs=5/hour in Karachi and marginal product is 28 at wage of Rs=4/hour in Gawdar?
