Units of Units of Labor, L Capital, K 1 2 3 4 1 50.0 66.7 75.5 80.0 2 66.7 100.0 120.0 133.3 3 120.0 150.0 171.4 200.0 75.0 4 80.0 133.3 171.4 This table illustrates a production function because capital and labor long-run; are used in equal increments short-run; can both be varied long-run; can both be varied O short-run; are used in equal increments
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- 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?Consider the augmented production function Y equals A K to the power of 1 divided by 3 end exponent open parentheses H N close parentheses to the power of 2 divided by 3 end exponent, where Y is output, A is total factor productivity, K is capital, N is the number of workers, and H is average years of education. Suppose that A=2, K=8, and N=1000. What is the average product of labor (or output per worker) if H is 15.7?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)
- Production Function. Consider the Cobb-Douglas production function discussed in class:F(K, L) = AK^1/3 L^2/3. Suppose that parameters are initially A = 1, K = 150, and L = 10. d) Suppose that the quantity of labor L doubles. Calculate Y, w, r, Y/L, and K/L. Com-ment on how and why these numbers changed relative to (c) and why they did so. E) Suppose that the quantity of capital K doubles as well. (So now both K and L aretwice their previous value). Calculate Y, w, r, Y/L, and K/L. Comment on how thesenumbers changed relative to both their initial values, and their values in (d).Suppose the production data of XYZ company mentions labor (L) as a variable input and machine (K) as a fixed input. Complete the table as XYZ increases its number of laborers (L). L TP MP AP 1 100 100 100 2 220 120 110 3 270 1) _____ 90 4 270 2)_____ 3)_____ 6 4)_______ 5)_____ 50 8 180 6) ____ 7) ____Suppose that government wishes to promote more capital intensive agriculture and subsidises agricultural capital equipment in order to achieve this. a) Using an isoquant map of the tradeoff between capital and labour, show how the reduced cost of capital will affect the individual farmer’s decision problem. b) Using a production function approach with labour as the variable input, show how the reduced cost of capital will affect the individual farmer’s decision problem. c) What overall effect on agricultural employment would you expect, given your answers in (a) and (b)?
- If output is produced according to Q = ( KL) 3/4, then this production process exhibits: a.first decreasing and then increasing returns to scale b.first increasing and then decreasing returns to scale c.increasing returns to scale d.decreasing returns to scale e.constant returns to scale Hedge Fun is a landscaping firm that specializes in topiary. Last year, the firm had 60 employees and served 120 customers. This year, it had 70 employees and served 140 customers. The average product of labor is at a maximum when the number of customers is: a.equal to 120 b.greater than 140 c.equal to 140 d.between 120 and 140 e.less then 120Please no written by hand and no image Suppose that the production function is given by Y=AK0.4N0.6. What is the percentage change in output if both capital and labor rise by 42%? Write the answer in percent terms with up to two decimals (e.g., 10.22 for 10.22%, or 2.33 for 2.33%).Let a firm's production function Q (L)=12L^2-1/20L^3 (i.e. output as TL orthe amount of production depends on the workforce, L, as Q is the number of people with a single production input). This functionlet be the foreground 0 ≤ L ≤ 200 for. Accordingly,A) What is the number of labour force (L*) that will make output (Q) the highest?B) what is the number of workers (L**) who will make the maximum amount of output per employee(i.e. Q (L)/L)?c) in both cases the output of the L* and L** values you find and the output per employee at the mosthow can you be sure it's high? Show me.
- L TP AP MP 0 0 1 35 2 80 3 122 4 156 5 177 6 180 1. Compute marginal products and average products of the various quantities of labour! 2. Made coclusions!3. First, do the following functions exhibit increasing, constant, or decreasing returns toscale? Why? Explain in detail. Second, calculate the marginal product of each factorand discuss what happens to the marginal product of each individual factor as that factoris increased and the other factor is held constant. a. q = 3L + 4Kb. q = (2L + 2K)1/3c. q = 2LK2d. q = L1/4K1/3e. q = 4L1/2 + 4KCowles Foundationfor Research in Economicsat Yale UniversityCowles Foundation Discussion Paper No. 2021ARE WE APPROACHING AN ECONOMIC SINGULARITY?INFORMATION TECHNOLOGY AND THE FUTUREOF ECONOMIC GROWTHWilliam D. NordhausSeptember 2015An author index to the working papers in theCowles Foundation Discussion Paper Series is located at:http://cowles.yale.edu/This paper can be downloaded without charge from theSocial Science Research Network Electronic Paper Collection:http://ssrn.com/abstract=2658259Electronic copy available at: http://ssrn.com/abstract=2658259Are We Approaching an Economic Singularity?Information Technology and the Future of Economic GrowthWilliam D. Nordhaus1September 1, 2015AbstractWhat are the prospects for long-run economic growth? The presentstudy looks at a recently launched hypothesis, which I label Singularity.The idea here is that rapid growth in computation and artificialintelligence will cross some boundary or Singularity after whicheconomic growth will…