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- Answer the Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output ifit the firm decides to triple both the amount of labor and capital?2. State the optimization problem of the firm.3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product ofCapital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combinationof K and L that the firm should use to produce the maximum possible output. Do not solvethe problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it faces?Q5 A firm's production function is Q is equal to 5L2Ka) Find out the MPL and MPb) Does this production function exhibit constant, increasing, or decreasingreturns to scale?c) What is the marginal rate of technical substitution of L for K for thisproduction function Q6.Suppose the firm sells its output according to the following demand scheduleMarginalTotal Product Total Revenue eLabor Product Price Revenue Product$3.50192c2.80182.30291.80391.65471.5021.4053Fill in the remaining two columns of the table. How many workers wilhired at a wage of $722/3- 1/3 Q1. Consider the production function Q = 9LK" a. What is the level of output when L 1000 and K = 216 b. Use marginal analysis to estimate Q(1000,216) and Q(1000,217.5) c. Compute.these two values of Q to three decimal places and compare these values with your estimate in (b) above. d. The demand funetjon Q = K,P,""P;"1" is ealled a constant clasficity demand function. Compute the three clasticities (Own price, Cross Price and Income) and show that they are all constant. %3D a12,b1
- Suppose Mr. Saad is a producer of Lola Loo chocolate, following is the information available of his production plant. Quantity of Labour (L) Quantity of 1 2 3 4 5 Capital (K) 10 15 25 100 50 20 30 40 50 75 50 75 100 125 150200250 300 75 90 105 120 2 30 50 62 15 If K and Lare imperfect substitutes and complements from the information above draw at least three isoquant (map) and identify the level of production. H73 41-a Suppose you have following production function for your firm : q = Ax;“x, where x, > 0, x, > 0 and a ± 0, a0. The price of input x, is w>0 and the price of x, is r > 0. a) Compute the marginal products of xi and x2. b) Using Lagrange method, write down cost minimization problem and first order conditions. c) Determine the conditional factor demands and cost function of the firm, x1* x2* and C* as a function of w, r, q and 2.Homework 2.1 Suppose a business manager of the factory wants to assess in terms of elasticity of demand, whetherthe products that his business is producing are complement goods or substitute goods inconsumption. So please explain which are the factors need to consider the long-run average cost curve in terms of usage of input?
- 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)Saxxon Fifth Avenue's production function is given by Q = L+ K. Let w = 1 and r = 2 be the prices of labor and capital, respectively. (a) Find the equation of Saxxon Fifth Avenue's longrun total cost curve. Hint: Note that labor and eapital are perfect substitutes. (b) Suppose capital is fized at 5 units (i.e., K = 5) in the short run. Derive the equation for Sazzon Fifth Avenue's shortrun total cost curve. For simplicity, assume the fxed cost is sunk. (c) In a graph, draw Saxon Fifth Avenue's short-run total cost curve and longrun total cost curve.Production. Assume a production with two variable inputs (L, K). Show graphically the following and explain: (a) fixed-proportions production function (b) inputs are perfect substitutes
- Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output if it the firm decides to triple both the amount of labor and capital?2. State the optimization problem of the firm.3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product ofCapital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combinationof K and L that the firm should use to produce the maximum possible output. Do not solvethe problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it faces?Which of the following is truc? (a) AFC + TO=ATC X (b) If total economic suiplus is negative due to a shift in a demand or supply curve, society is better 6ff (c) The law'of diminishing marginal refurns states that as the use, of an input increases, its MPP will never fall, instead will continue tò increase None of the above1.Suppose a chair manufacturer is producing in the short run (with its existing plant andequipment). The manufacturer has observed the following levels of production correspondingto different numbers of workers:Number of Workers Number ofChairs 1 10 2 18 3 24 4 28 5 30 6 28 7 25a. Calculate the marginal and average product of labor for this production function.b. Does this production function exhibit diminishing returns to labor? Explain.c. Explain intuitively what might cause the marginal product of labor to becomenegative.