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- Given the production function f(x,x2) x,ax,, calculate the profit maximizing demand and supply functions, and the profit function. ii. %3D4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…4) A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP(1/3)*LN(1/5) per hour, where capital (K), production labor (LP), and non-production labor (LN) are input factors used in production. The firm operates in a competitive market, where they are a price taker within the capital & labor markets and its own price (r = 40, wP = 25, wN = 50, P = 20). Answer the following.a. If capital and non-production labor are fixed at K = 32 and LN = 243, what is the general form MPLP and graph Q wrt to LP changing [you do not need to solve for LP yet].b. Is this production function decreasing, constant, or increasing returns to scale and why.c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number of LP to employ to maximize profits and the quantity produced (VMPLP = wP).d. If the firm can control both K and LP, what does the Isoquant curve look like and its slope in relative terms if LN is fixed at 243 units [IQ slope =…
- Juan Valdez owns a coffee farm in Colombia. His production function is: f(x1,x2)=(x1−1)^0.25 x2^0.5 Assume the price of input 1 is r and the price of input 2 is w. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm?What is the elasticity of substitution for the production function f(K, L) = K¹/4 [³/4? (a) o = 1 (b) o = -1 (c) o = 1 (d) σ = 3 2There is a firm making custom stuffed animals. The demand function for custom stuffed animals is: P = 1000 - 20Q The cost depends on how much of each of their inputs they use. It takes 3 inputs to make a stuffed animal: cotton, oil, and chorizo. The amount required, input prices, and restrictions are below: It takes 1 pound of cotton to make a stuffed animal. Cotton costs $20 per pound. They can buy up to 23 pounds of cotton. It takes 2 barrels of oil to make a stuffed animal. Oil costs $10 per barrel. They can buy up to 44 barrels of oil. It takes 3 chorizo burritos to make a stuffed animal. Burritos cost $5 per burrito. They can buy up to 100 burritos. Set this up in Solver to help them maximize profit by choosing the best quantity of stuffed animals to produce, subject to the constraints of the maximum amount of cotton/oil/burritos they can buy. In the space below, tell the profit that the firm will earn when they maximize its profit. PLEASE SHOW EXCEL WALKTHROUGH USING SOLVER.…
- A firm is able to adjust both L and K and has a production function q = KL, where K is the amount of capital and L is the amount of labor it uses as inputs. The cost per unit of capital is r and the cost per unit of labor is w. The (conditional) demand for capital (also known as the optimal level of capital) is given by: O qwr O the square root of qr/w O qw/r O q/wr O the square root of qw/rDoes the value of λ change if the budget changes from $4600 to $5600?What condition must a Cobb-Douglas production function q = cKαW β satisfy toensure that the marginal increase of production is not affected by the size of thebudget?Consider a production function of three inputs, labor, capital, and materials, given by Q = LKM. The marginal products associated with this production function are as follows: MPL = KM, MPK = LM, and MPM = LK. Let w = 5, r = 1, and m = 2, where m is the price per unit of materials.a) Suppose that the firm is required to produce Q units of output. Show how the cost - minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of capital depends on the quantity Q. Show how the cost - minimizing quantity of materials depends on the quantity Q. b) Find the equation of the firms long-run total cost curve.c) Find the equation of the firms long-run average cost curve.d) Suppose that the firm is required to produce Q units of output, but that its capital is fixed at a quantity of 50 units (ie., K 50). Show how the cost- minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of materials depends on the quantity Q. e)…
- A firm has the following production function Y=(x_1^α+x_2^α )^(1/2α) Obtain the conditional demand functions for x1 and x2 given a level of output q.Consider the production function: Y = 0.75X + 0.0042X2 – 0.000023X3 If input price is 0.15$ and output price is 4$ then at what level of X, profit will be maximum?b Now suppose Q = 2L +3K. Let the market price of L be w = 5 and the price of K be r = 4. Let both L and K can vary with production. Compute the input demand functions as a function of Q. (4 Points) c Calculate the marginal cost and average cost of the above function in subpart (b). Show them graphically. At what prices of textile will the producer shut down production. (3 Points) d Now suppose Q = 10LK. The market prices of inputs are as in subpart (b) above. Compute the input demand functions as a function of Q. Find the optimal production when the price of textile is $10 per yarn. (5 Points)