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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 $72Constrained 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?
- 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?69. If the price of labor falls relative to the price of capital, and as a result the quantity of capital employed decreases, it can be concluded that: A. The substitution effect is greater than the output effectB. The output effect is greater than the substitution effectC. The income effect is greater than the output effectD. Labor cannot be easily substituted for capital8) Suppose the production function for good q is given by q=3 ∙K+2∙ L where K and Lare capital and labor inputs. Consider three statements about this function:I. The function exhibits constant returns to scaleII. The function exhibits diminishing marginal productivities to all inputsIII. The function has a constant marginal rate of technical substitutionWhich of these statements are true?A) All of themB) None of themC) I and II but not IIID) I and III but not IIE) Only I .
- 1.A 15 per cent increase in all inputs leads to only a 5 per cent increase in the output. Are the returns to scale increasing, constant or diminishing? Illustrate your answer2.What is the slope of an iso-cost line equal to and why? Provide mathematical explanation3.“By definition, cost is zero if a firm does not hire any input. Hence cost-minimization essentially means shutting down the operation of the firm.” Do you agree with the statement? Justify you answer by giving an explanation from microeconomic theory.4.What is meant by an expansion path? Illustrate expansion paths for a normal input and an inferior input.The manager's job in leading the previously mentioned production process is twofold: (1) toguarantee that the company works on the production function, and (2) to ensure that thebussiness employs the appropriate level of inputs. Justify how these two factors contribute tothe company operating at he optimal position the production function.A. Explain how MP = decreasing within the Cobb - Douglas function ( explain the functions and their variables ) 2.45 2.65 B. The company Tres Monjitas faces the following production function : Q = L K and has the following prices of inputs : PL = $ 10 and PK = $ 20 . Estimate the Cobb - function Douglass (Get L relative to K).
- 38. For the production function y = 3x₁ + 4x2 , which of the two inputs is more productive when x₁ is 1 and x₂ is 10 ? O. X1 O. X2 O. neither ; for this situation , they have equal marginal products O. cannot tell from the above information 39. Given the production function y = 3x₁ + 4x2 , what is the marginal rate of technical substitution of x₁ for x₂ ( MRSx1x2 ) when x₁ is 5 and x₂ is 5 ? O. -0.75 O. -x1 / 5 O. 5 O. -5Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 6 and r = 4. These prices then shift to w = 4 and r = 2.a. In which direction will the substitution effect change the firm’s employment and capital s tock?b. In which direction will the scale effect change the firm’s employment and capital stock?c. Can we say conclusively whether the firm will use more or less labor? More or less c apital?1. A firm’s production function is , where Ldenotes the size of the workforce. Find the value of MPLin the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form where A and n are positive constants. 3. The demand and total cost functions of a good arerespectively and a) Find expressions for TR, (profit) , MR, and MC in terms of Q. b) Solve the equation and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢1/4 million per floor (c) Specialized costs of GH¢10000x per floor. How many floors should the office complex contain if the average cost per floor is to be minimized? 5. The supply…