Consider an economy where labor is the only factor of production. The aggregate production function is given by F(L) = 7L04. All markets are competitive. Suppose the supply of labor is given by L = 37.Compute the equilibrium labor share of the economy.
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- Question 5: Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 500 bottles per day (i. e. MPK = 500). An additional man-hour of labor would increase output by 1000 bottles per day (i. e. MPL = 1000). The price of a man- hour of labor is $50 per hour. The price of a machine-hour of fermentation capacity is $5 per hour. 1. Is the brewery currently minimizing its cost of production? Check using the minimization condition. 2. It turns out, the brewery is not optimally chossing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease? 3. Suppose that the price of a machine-hour of fermentation capacity rises to $25 per hour. How does this change the answer from part 1?Consider a production function of three inputs, labor, capital, and materials, given by Q = LKM. The marginal products associated with this production function are as follows: MPL = KM, MPK = LM, and MPM = LK. Let w = 5, r = 1, and m = 2, where m is the price per unit of materials.a) Suppose that the firm is required to produce Q units of output. Show how the cost - minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of capital depends on the quantity Q. Show how the cost - minimizing quantity of materials depends on the quantity Q. b) Find the equation of the firms long-run total cost curve.c) Find the equation of the firms long-run average cost curve.d) Suppose that the firm is required to produce Q units of output, but that its capital is fixed at a quantity of 50 units (ie., K 50). Show how the cost- minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of materials depends on the quantity Q. e)…The following are correct descriptions about the concept of Marginal Productivity of Labor (MPL), EXCEPT: Question 1 options: MPL measures the extra production generated by adding one extra unit of labor. MPL initially increases and eventually declines as more units of Labor are added. From the producer's perspective, The optimal level of labor is the one when MPL = Market Wage and MPL is still Increasing. If MPL increases for any given amount of labor, it will lead to a shift up of the Demand for Labor.
- Question 1: Consider the following production function that depends only on labor:Q = 81¹/2 1. Write a combination of input and output that are technically efficient. In other words, for what level of L and Q, is the technology efficient? 2. Write a combination of input and output that are technically inefficient. In other words, for what level of L and Q, is the technology inefficient? 3. Write a combination of input and output that are technically unattainable. In other words, for what level of I and Q, is the technology unattainable?Consider the following production function q = F (L, K) = L²K What is the marginal rate of substitution (MRTS=-MPL/MPK) when L=K=1? (MRTS is negative)Question 5: Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 500 bottles per day (i.e. MPK = 500). An additional man-hour of labor would increase output by 1000 bottles per day (i.e. MPL = 1000). The price of a man-hour of labor is $50 per hour. The price of a machine-hour of fermentation capacity is $5 per hour. 2. It turns out, the brewery is not optimally chossing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease?
- Consider the following production function: f (A, B) = gamma multiply A^alpha multiply B^Beta. where A and B are the inputs and alpha, Beta, gamma are in the set (0,1). Let wA and wB the price of the two inputs. Assume wA, wB > 0. Is the production function separable?Does the production function exhibit constant returns of scale?Compute the cost function and the conditional input demand function.How do these three functions react to a change in wA? Suppose the price of both inputs double, what happens to the conditional input demand function? And to the cost function? Suppose the desired level of output double, what happens to the conditional input demand function? And to the cost function?…Economics Suppose that firms face the following production function: Q = L + K + 2L ^ (1/2) * K ^ (1/2) This production function exhibits information that is not enough to determine Returns to Scale Increasing Returns to Scale Decreasing Returns to Scale Constant Returns to ScaleConsider a firm that produces widgets according to the following Cobb-Douglas production function: Q = A * L^α * K^β where: Q is the quantity of output, L is the quantity of labor, K is the quantity of capital, A is a scale parameter (total factor productivity), α and β are the output elasticities of labor and capital respectively. Given that A = 1, α = 0.6, β = 0.4, L = 16 and K = 9, a) Calculate the quantity of output Q. b) If the firm increases the quantity of labor (L) to 20 while keeping the quantity of capital (K) constant, what will be the new quantity of output?
- Suppose that the process of producing mozzarella sticks is described by the following production function: Q = KL^2. If the price of renting shaping machine is $10 and the price of hiring labor is $15. What is the capital output ratio?Consider the following production function: Q = 3K + 6L where K is Capital, L is Labour and Q represents output. What kind of production function (perfect substitutes, imperfect substitutes, perfect complements etc) does this equation represent? Explain your answer clearly.QUESTION 8 Consider the production function F(A,K) = A*In(K), where A = 3 is a constant. What is the marginal product of capital equal to when K = 2? (State your answer to 2 decimal places.)