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- 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)The work force of a certain factory is growing at rate of 2 per month while the average productivity of a worker is growing at a rate of 4 units per month. If the work force is currently 100 and the average productivity per month is 200 units, at what rate is the total productivity per month of the factory increasing? (a) What happens if the work force is declining by 2 per month? (b) What happens if the average productivity is decreasing by 5 per month?A firm spends 1.000 pesos regardless of how much output is produced. Every worker hired by the firm receives a wage of 1,200 pesos. We also know that: L TP AP MP TFC TVC TC AFC AVC AC MC 0 0 1 50 2 104 3 162 4 224 5 282 6 336 7 386 8 432 9 474 10 512 11 546 12 576 13 602 14 624 15 640 Where L =…
- A firm spends 1.000 pesos regardless of how much output is produced. Every worker hired by the firm receives a wage of 1,200 pesos. We also know that: L TP AP MP TFC TVC TC AFC AVC AC MC 0 0 1 50 2 104 3 162 4 224 5 282 6 336 7 386 8 432 9 474 10 512 11 546 12 576 13 602 14 624 15 640 Where 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…QUESTİON: Assume that we have a Cobb-Douglas type aggregate production function in the form: where : W=technology and r is standard share parameter of Cobb-Douglas production function.a. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from the previous question (Question-1)?
- Question 27Refer to Figure 1. Suppose the per-worker production function in the figure above represents the production function for the U.S. economy. If the United States decided to double its support of university research, this would cause a movement fromn.P232,P5) Hey! Need help with the following macro question, thank you in advance! (chart attatched below) Suppose Die Cast Aluminum Co. is a subcontractor for the auto industry and makes specialized auto parts. There is a bracket it manufactures that it sells for $1.50. The following table shows the number of brackets that can be produced from a given number of labor hours. Assume that the company cannot hire labor for a fraction of an hour. Find the marginal product (in brackets), and the value of the marginal product (in dollars), of each hour of labor. If the wage paid to workers in Die Cast’s plant is $25 per hour, how many hours of labor should the firm employ? How many hours will be employed if the wage increases to $35 per hour? Explain. How many hours will be employed if the wage is $35 per hour, but the price of a bracket declines to $1?Can you put a solution to this? Instruction: (see other instructions below, for the submission of answer sheet) A. Complete the Column for MRS. Show your solution for each answer, Number each solution that corresponds to each unknown MRS. B. Graph the Labor-Capital function, making sure that Labor units are in the horizontal axis MRS = change in K/ change in L change in K = final K - initial K change in L = final L - initial L MRS = 26-30 /2-1 MRS = -4/1 MRS = - 4 Units of Labor Capital MRS 1 30 0 2 26 -4 3 22.5 (1) 4 19.5 (2) 5 17 (3) 6 15 (4) 7 13.5 (5) 8 12.5 (6) 9 12 (7) 10 12 (8)
- Q 1. Given the following production function Where; Y is the total output of the economy K is the amount of land, and L is the labor force of the economy Assume A=1 and = 0.5 The initial values of K and L is 100 units. a. How much output does the economy produce? b. What are the wage and rental price of land? c. What share of output does land receive? d. If a flood damaged half of the land, what is the new level of output in the economy? e. What is the new level of wage and rent? f. What share of output does land receiving now? Q 2. Suppose in an economy, people hold currency worth of 10,000 Rs and 4000 Rs worth of demand deposits in the only bank. The reserve-deposit ratio is 20%. a. What is money supply, monetary base and money multiplier? b. Suppose the economy only bank is a simple bank. It takes deposits and make loans and has no capital. Show the balance sheet of the bank. c. The central bank wants to increase the money supply. Should it buy or sell the Govt bonds in the…Suppose the production function is Y = AK0.3N0.7. Suppose in 2010, K = 1000, N = 100, and Y = 199.5. In 2020, capital, labor, and output have doubled, so K = 2000, N = 200, and Y = 399. (a.) By what percentage did productivity grow from 2010 to 2020? (b.) If output had risen to 798 instead of 399, and capital and labor doubled, by what percentage would productivity have grown from 2010 to 2020?hy does a measure of labor productivity—the output produced per worker– rise for many firms during recessions? During the boom years period of 2005through November 2007, the annual average output per worker was lower in U.S.manufacturing than during the Great Recession of 2007–2009 as well during therelatively low-demand years since then through 2013.Firms produce less output during recessions as demand for their products falls.Consequently, firms typically lay off workers during recessions. Thus, whetheroutput per worker rises or falls depends on whether output or employment fallsby more. The labor productivity pattern over the business cycle differs across in-dustries. If we know about a firm’s production process, can we predict whetheroutput produced per worker will rise or fall with each additional layoff?
