) Suppose there are two inputs in the production function-labor and capitaland that these two inputs are perfect substitutes. Suppose that the price of capital is 750 GHC per machine per week and that the weekly salary of each . worker is 300 GHC . i) Draw the isocost line ii) With the aid of a graph, explain the effect of a wage decrease on flrm-level employment and output holding initial cost ouday constant.
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) Suppose there are two inputs in the production function-labor and capitaland that these two inputs are perfect substitutes. Suppose that the
. i) Draw the isocost line
ii) With the aid of a graph, explain the effect of a wage decrease on flrm-level employment and output holding initial cost ouday constant.
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- please sir solve these 3 questions 33- If an increase in the price of one good leads to a fall in the quantity demanded of other than these goods are complementry good A- True B- False 34- the production function is a purely technical relationship between input and output A- True B- False 35- marginal proudact is defined as the change in TP resulting from the employment of an additional unit of a varibal factor: A- True B- FalseSuppose a firm is producing some output level q1 using a combination of capital and labor for which the RTS (MPL/MPK) at this input combination is 1. Suppose further that the wage rate is $20 and the rental rate on capital is $10. Which of the following statements is correct? A. The firm can reduce its costs of producing q1 by using more labor and less capital B. The firm can reduce its costs of producing q1 by using more capital and less labor C. The firm is currently minimizing the costs of producing q1 D. Whether or not the firm is minimizing the costs of producing q1 is indeterminateConstrained 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?
- Consider 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?Non-backward-bending labor supply curve. Consider an economy populated by 100 individuals who have identical preferences over consumption and leisure. In this economy the aggregate labor supply curve is upward-sloping. For simplicity, suppose that throughout this question that the labor tax rate is zero. a. For such a labor supply curve, how does the substitution effect compare with the income effect? b. Using indifference curves and budget constraints, show how such a labor supply curve arises.Production function for firm is Ys=ln(Ld)Utility function is U(Yd, Ld)= Ys+ln(1-Ls)1) Write down maximization problem of firm and find labor demand curve2) Write down maximization problem of household and find labor supply curve3) Write down market clearing conditions4) Calculate equilibrium employment and real wage5) If the price is equal to $2, what would be the nominal wage in equilibrium
- Suppose that this conveyor-manufacturing firm has another location and would like you to evaluate the input mix decisions at this new location. Here is all you know about the newlocation. The marginal rate of technical substitution is currently 0.5. The marginal product of labor at its target level of output is 60 rollers per hour. What is the marginal product of capital? Ifthe rental rate for capital is $24 per hours at this location and the wage paid to labor is $12 per hour, could this location be minimizing the costs of producing its target level of output? Explain briefly.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?Consider the following production functions, to be used in this week’s assignment:(A) F(L, K) = 20L^2 + 20K^2(B) F(L, K) = [L^1/2 + K^1/2]^2For each of production functions (A) and (B) given above, do the following steps.(i) Calculate the marginal product of labor MPL(L, K) = ∂F(L, K) / ∂L.(ii) Calculate the marginal product of capital MPK(L, K) = ∂F(L, K) / ∂K.(iii) Calculate the absolute value of the technical rate of substitution as the ratio of marginal products andsimplify as far as possible: |TRS(L, K)| = MPL(L, K) / MPK(L, K). PLEASE SHOW ALL WORK
- Consider the following model of the factors that influence a person's annual wage: Y = β0 + β1X1 + β2X2 + β3X1X2 + β4X3 + u where Y = annual wage, in dollars X1= years of formal education X2 = age, in years X3 = variable equal to 1 if male, 0 otherwise U = error term Which of the following is the interpretation of β1 alone? The effect of X1 on Y when X2 = 0 The effect of X1 on Y when X2 is at its median value. The effect of X1 on Y, holding all else equal. The effect of X1 on Y when X2 is at its mean value.It deals with the Production Function, Marginal Rate of Technical Subsition . Problem: The Production Function for a Product is given by q=10 K ^1/2 L^1/2 where K is capital and L is Labor and q is output . 1a. Find the Marginal Product of labor and the Marginal Product of Capital 1b. Find the Marginal Rate Of Technical Substitution between Labor and Capital 1c. Denote the wage of Labor by w and the renal of cpaital by r . What is thre cost of the minization condition for a firm . Show it digrammatically.Assume that tighter immigration laws cause a reduction in the supply of agriculturalworkers and this leads to higher wages in the sector. Dean’s Fruity Produce Ltd, afarm in Leicestershire, uses two inputs to harvest its output – machines (capital) andagricultural workers. Dean, the managing director of the company, has employedKarishma (a brilliant statistician) and she has estimated that the business’s long-runwage elasticity of labour demand is -1.7. Using isoquant/isocost analysis, explain the possible impact of the higher wages on the output level, total cost of production and input-factor mix of this business in boththe short and long-run and how would your answer change if Karishma had estimated that the long-run wageelasticity of labour demand was -0.4? (1000 words)