The output, Q, of a car factory, may be modeled by a Cobb-Douglas production function, Q = AKm Ln, which is known to display constant returns to scale. The output is 800 when K = 1 and L = 1, and the output is 3658 when K = 10 and L = 3. Find the values of A, m, and n. Round your answers to two decimal places if necessary. A = m= and n=
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- Galaxy, a multinational corporation, has two plants, one in the United States and the other in Mexico, and it cannot change the size of the plants or the amount of capital equipment in the short run. The wage in Mexico is equivalent to US $5 per hour. The wage in the U.S. is $25 per hour. Given current employment situation, the productivity per worker in Mexico is 200 units per hour, and the productivity per worker in the U.S. is 400 units per hour.Is Galaxy maximizing output relative to its labor cost? If not, what should Galaxy do? Justify yourPlease indicate whether the following production function has the characteristic of CRS, IRS and DRS.F(K, L) -[aKρ+(1-a)Lρ]1/ρ, (1›a>0, 1> ρ) A.IRSB. DRSC. CRSA Cobb-Douglass production function is estimated as logQ = 2 + 0.52logK + 0.46logL. The interpretation ofthe coefficient 0.52 is thata. 1 unit increase in K will lead to 0.52 units increase in Q.b. 1% increase in K will lead to 52% increase in Q.c. 0.52% increase in K will lead to 1% increase in Q.d. 1% increase in K will lead to 0.52% increase in Q.
- 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?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 β is larger than, smaller than, or equal to one?I'm curious on how to calculate the SR production function, what I know is q = 20K^.3L^.7 and r = 2 and w = 33 and the K is fixed at 300.
- Returns to scale in production: Recall that a production function F(K, L) exhibits constant returns to scale if doubling the inputs leads to a doubling of output. If it leads to more than doubling of output, there are increasing returns to scale; if it leads to less than doubling of output, there are decreasing returns to scale. The answers to parts (a) and (f) are worked out below. (a) Y = K1/2L1/2. If we double K and L, output is (2K) 1/2(2L) 1/2 = 21/221/2K1/2L1/2 = 21/2+1/2K1/2L1/2 = 2K1/2L1/2. So output exactly doubles, and there are constant returns to scale. (b) Y = K1/3L2/3 + . This production function says you get units of output “for free,” that is, even if there is no capital and no labor. Then you produce on top of that with a Cobb-Douglas production function. If we double K and L, output is Notice that the first term is doubled, but the output we got for free (the A) is left unchanged. Therefore, output is less than doubled, and this…Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=W.Kr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from previous question (Question-1) (Y=Ka.Lb) ? (Question 1: Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=Ka.Lb )A firm produces using a production function given by F(K, L)=ln(K42+40L). The firm employs 100 workers. The nominal wage rate is 10 and the price of its good is 2. The firm can increase its profit by a) Hiring more workers b) Firing some of its workers c) It is already at the maximum profit d) We need to know the amount of capital to know how many workers it should hire
- Consider a Cobb-Douglas production function, Y=zKα(Nd)1−α, with 0< α <1. (a) Show that this production function exhibits constant returns to scale. (That is, show that when K becomes xK and Nd becomes xNd, Y becomes xY for x > 0. (b) What is MPN? Is it increasing or decreasing in Nd?y = F(L,K) = min(L,3K) Show if the leontief production function displays constant returns to scale.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…