in an economy with production function Y = 1.5 × K^0.3L^0.7, K = 343, and L = 512. If factor markets are in equilibrium, then the rental price of capital is (approximately) ________, and the real wage is (approximately) ________. A) 0.5; 0.8 B) 7; 8 C) 0.9; 1.35 D) 1.4; 0.4 E) 0.6; 0.9
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in an economy with production function Y = 1.5 × K^0.3L^0.7, K = 343, and L = 512. If factor markets are in equilibrium, then the rental price of capital is (approximately) ________, and the real wage is (approximately) ________. A) 0.5; 0.8 B) 7; 8 C) 0.9; 1.35 D) 1.4; 0.4 E) 0.6; 0.9
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- 11. Suppose that the production function is Y=K^(0.5) N^(0.5). With this production function the marginal product of labor is MPN=0.5K^(0.5) N^(-0.5). The capital stock is K=100. The labor supply curve is NS=100(w^2), where w is the real wage and NS denotes the quantity of labor supplied. Compute the equilibrium level of employment (N). 12. Consider Question 11 again. Compute the level of full-employment output (Y). Approximate your answer to the next integer. 13. Consider Question # 11 again. Due to a temporary reduction in immigration, the economy's labor supply curve changes to NS=90(w^2). A policy maker suggests that in order to increase full-employment output in response to the reduction in immigration the government might temporarily subsidize the firm's labor cost by paying a fractions of the wage it pays to a worker. That is, if the real wage received by a worker is w, the firm only pays a portion (1-s)w with the remaining sw coming from the government. Compute the subsidy s…Suppose that a certain factory output is given by the Cobb-Douglas production function ?(?, ?) = 60?^1/3?^2/3 units, where K is the level of capital and L the size of the labor force need to maximize the factory’s output. (a) Determine whether the Cobb-Douglas production function is concave, convex, strictly concave, strictly convex or neither.The production function in an economy is. Y = 5(4.00N-0.0188N²), where the marginal product of labor is given by: MPN = 5(4.00 -0.0376N). The equation for the labor supply curve is: NS = 48.0 + 8(1 - t)w, where NS is the amount of labor supplied, w is the real wage and t is the tax rate on wage income. The tax rate is t = 0.20. Determine the labor demand function. (Enter your responses rounded to two decimal places); -0-0w ND=
- Suppose that a firm's production function is Cobb-Douglas (Y = A K\alpha L1 - \alpha) with parameter a \alpha = 0.4. a) What fractions of income do capital and labor receive? b) Suppose that number of the labor increases by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage? c) Suppose that a gift of capital from abroad raises the capital stock by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage? d) Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage?1. Consider a static labour supply model for an individual. Assume that the person works a positive number of hours. Assume that the utility function is of the following form: U=x0.5 +8(T-h)(0.5) where x is consumption and his hours of work, and 8 is a parameter of the utility function. The person is paid a wage of w for each hour worked. The person has no other source of income other than employment earnings. Assume that the price of x equals 1. a) Specify the utility maximization problem, write down the Lagrange function, and solve for the first order conditions. b) Solve for the MRS condition between consumption and hours of work. c) Assume that 8=2 if the person has a child living at home, and 8=1 otherwise. Explain (and either show mathematically or graphically) how this will affect the optimal number of hours of work of the person.If the production function for GDP is Cobb-Douglas in labour and capital, with the exponent on capital is a space equals space 1 third, and assuming constant returns to scale, and a perfectly competitive goods market a. The marginal product of labour (vertical axis) will have a positive, concave slope when plotted against labour (horizontal axis) b. In equlibrium, wage will equal 2 over 3 y, where y is output per worker c. Labour and capital are complements so the derivative fraction numerator d squared Y over denominator d L d K end fraction less than 0 d. None of the answers is correct e. The marginal product of labour is: left parenthesis 1 minus a right parenthesis A open parentheses Lover K close parentheses to the power of a
- Suppose a manufacturing firm currently employs 100 workers and the wage rate is $20 per hour. The firm's production function is given by Q = 10L^(1/2), where Q represents output and L represents the number of workers. Calculate the firm's current MPL .You are a manager for a company that manufactures office furniture. To estimate the production function for a particular line of office chairs, you hired an economist to work with engineering and operations experts. The report from these experts indicates that the relevant production function is ? = 2?½?½ where K represents capital equipment and L is labour.Workers at the firm are paid a competitive wage of 120 cedis per day and chairs can be sold for 400 cedis each. a. Your company has already spent a total of 8,000 cedis on the 9 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility needed to acquire additional equipment. i. Is this firm operating in the short-run or in the long-run? Explain your choice. ii. what is your profit-maximizing level of output and labour usage? iii. What is your maximum profit?Consider the following production function: Assume capital is fixed at K = 25. At what level of employment does the marginal product of labor equal zero? The marginal product of labor equals zero when L= q=48LK+20L2 3 (3) ₁³. (Enter a numeric response using an integer.)
- Q1. Suppose we are given the constant returns-to-scale CES production function q = [k + l]1/ where k represents capital and l represents labora. a. Show that MPk = (q/k)1 and MPl = (q/l)1 . b. Show that RTS = (k/l)1 ; use this to show that elasticity of substitution between labor and capital= 1/(1 – ). c. Determine the output elasticities for k and l; and show that their sum equals 1.Note: Output elasticity measures the response of change in q to a change in any input. Elasticity of output wrt k is eq,k = %q/%k = (q/k)*(k/q) or (q/k)*(k/q) or lnq/lnkSimilarly for elasticity of output wrt l, eq,ld. Prove that q/l = (q/l) and hence that ln(q/l) = ln(q/l)Q1. Suppose we are given the constant returns-to-scale CES production function q = [k + l]1/ where krepresents capital and l represents labora. Show that MPk = (q/k)1 and MPl = (q/l)1 .b. Show that RTS = (k/l)1 ; use this to show that elasticity of substitution between labor and capital= 1/(1 – ).c. Determine the output elasticities for k and l; and show that their sum equals 1.Note: Output elasticity measures the response of change in q to a change in any input.Elasticity of output wrt k is eq,k = %q/%k = (q/k)*(k/q) or (q/k)*(k/q) or lnq/lnkSimilarly for elasticity of output wrt l, eq,ld. Prove that q/l = (q/l) and hence that ln(q/l) = ln(q/l)Q2. Suppose the production of airframes is characterized by a CobbDouglas production function: Q =LK. The marginal products for this production function are MPL = K and MPK = L. Suppose the price oflabor is $10 per unit and the price of capital is $1 per unit. Find the cost-minimizing combination of labor and capital if the manufacturer wants to…0.25 0.75 q=LK The wage rate (w) is $10 and the rental rate Suppose that a firm had a production function given by: (r) is $5. Calculate the amount of labor the firm would hire when it produces 400 units of output in a cost-minimizing way. (Round to the nearest 2 decimal places if necessary.) Answer: