A6 (a) If economy A grows annually at a rate of 1% and economy B grows annually at arate of 2%. Calculate the ratio of the GDP of economy B to economy A after 25years.(b)Consider the aggregate production function Y = K0.2 (AN) 0.8 Compute outputwhen K 100,000, A = 3, and N = 81.=(c)The Solow residual is given by TFP = 9y [agn + (1-a)gk]. Assume that theshare of labour is a = 0.8, and that the growth of employment is gCalculate the growth in output due to growth in employment.= 0.04

(a) If economy A grows annually at a rate of 1% and economy B grows annually at a rate of 2%. Calculate the ratio of the GDP of economy B to economy A after 25 years. (b) Consider the aggregate production function Y = K2 (AN) 0.8 Compute output when K 100,000, A = 3, and N = 81. = (c) The Solow residual is given by TFP = gy[agn + (1-a)gk]. Assume that the share of labour is a = 0.8, and that the growth of employment is g = 0.04. Calculate the growth in output due to growth in employment.

(a) If economy A grows annually at a rate of 1% and economy B grows annually at a rate of 2%. Calculate the ratio of the GDP of economy B to economy A after 25 years. (b) Consider the aggregate production function Y = K2 (AN) 0.8 Compute output when K 100,000, A = 3, and N = 81. = (c) The Solow residual is given by TFP = gy[agn + (1-a)gk]. Assume that the share of labour is a = 0.8, and that the growth of employment is g = 0.04. Calculate the growth in output due to growth in employment.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 8E

See similar textbooks

Similar questions

Assume that the production function for a country is given by Y=√K and annual investment is given by the function I=γ×YI where γ=0.280, and that the yearly depreciation rate is 4.67%. Suppose that this year, the output in the country is 1, and a neighbor country's output is 50% higher. Calculate the time it would take for the country's output to catch up with its neighbor's output. Assume the neighbor country's economy is neither growing nor shrinking.
Consider the following Cobb-Douglas production function for the bus transportation system in a city: Q = Lβ1Fβ2Bβ3Where L = labour input in worker hours F = fuel input in gallons B = capital input in number of buses Q = output measured in millions of bus miles Suppose that the parameters (α, β1, β2 and β3) of this model were estimated using annual data for the past 25 years. The following results were obtained: β1 = 0.45, β2 = 0.20 and β3 = 0.30a. Determine the (i) labour, (ii) fuel, and (iii) capital-input production elasticities .b. Suppose that labour input (worker hours) is increased by 2 percent next year (with the other inputs held constant), determine the approximate percentage change in output. c. Suppose that capital input (number of buses) is decreased by 3 percent next year (which, certain older buses are taken out of service). Assuming that the other inputs are held constant, determine the approximate percentage change in output. d. What type of returns to scale appears…
Solve for the steady state of K with: An Investment (I) function with a rate of growth of 0.4 times the square root of K and a depreciation (D) function of 0.03 * K. Now graph what this looks like. Hint: you need to set the production function equal to the depreciation function and solve for k.
Consider an economy’s production function is Y=K^1/3 N^2/3 and that both the saving rate and the depreciation rate are equal to 0.15. A. What is the steady-state level of capital per worker? B. What is the steady-state level of output per worker? Now suppose that the economy has reached its steady-state in period t, and then, in period t+1, the saving rate doubles to 0.30. The depreciation rate remains constant at 0.15. C. Solve for the new steady-state levels of capital per worker and output per worker. D. Calculate the path of capital per worker and output per worker over the first three periods after the change in the saving rate.
Question 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].
Consider the Production Function: Y=0.5√K√N a) Derive the steady-state levels of output per worker and capital per worker in terms of the saving rate (s) and the depreciation rate.b) Derive the equation for steady-state output per worker and steady-state consumption per worker in terms of the saving rate (s) and the depreciation rate.c) Suppose depreciation is 5% and savings rate is 10%. Calculate the steady-state output per worker.d) Now suppose the savings rate increases to 20%. What is the new steady-state output per worker?
Q: Determine whether the following statemnts are true or false: a) If the firm increases the volume of used resources by 30%, and the volume of production thus increases by 20%, then there is a positive effect of the production scale. b) Average fixed costs decrease as production increases. c) The economic profit usually exceeds the accounting profit.
Consider the following Cobb-Douglas production function for the bus transportation system in a city: Q = Lβ1Fβ2Bβ3 Where L = labour input in worker hours F = fuel input in gallons B = capital input in number of buses Q = output measured in millions of bus miles Suppose that the parameters (α, β1, β2 and β3) of this model were estimated using annual data for the past 25 years. The following results were obtained: β1 = 0.45, β2 = 0.20 and β3 = 0.30 a. Determine the (i) labour, (ii) fuel, and (iii) capital-input production elasticities
1. The Primary Metals production function in Table 7.4 of the MMH textbook, holding nonproduction workers constant, can be roughly expressed as Q = 100*L.08*K.37. Use this function to answer the following. Suppose a firm wishes to produce 1200 units of Q. Use an Excel Spreadsheet to find the MRTSLK in adding a 10th unit of Labor. Conduct your analysis using an Excel Spreadsheet and changing Labor by 1, 2, 3, etc., that is, use integer values of L only. In absolute value terms, the MRTSLK when we add the 10th unit of L is ______. A. 114.9. B. 18.4. C. 11.6. D. 7.5. E. 3.6. 2. This is a continuation of the previous problem. Suppose a Primary Metals company’s ratio of PL to PK is 1.40. What is the optimal (cost minimizing) combination of L and K that should be employed by the firm to produce Q = 1200? Conduct your analysis using an Excel Spreadsheet and changing Labor by 1, 2, 3, etc., that is, use integer values of L only. Use a Spreadsheet and not Excel Solver. The optimal L = _____…
Show that the two-input CES production(attached) has DRS, CRS, or IRS depending on whether B (beta) is smaller than, equal, or greater than 1.
Consider the Production Function: Y=√K√N a) Derive the steady-state levels of output per worker and capital per worker in terms of the saving rate (s) and the depreciation rate.b) Derive the equation for steady-state output per worker and steady-state consumption per worker in terms of the saving rate (s) and the depreciation rate.c) Suppose depreciation is 5% and savings rate is 10%. Calculate the steady-state output per worker.d) Now suppose the savings rate increases to 20%. What is the new steady-state output per worker?
firm decides to invest X units of capital in Project A and Yunits of labour in Project B. iv. The expected return for each unit of investment is $500 in Project A and $1500 in Project B. However in order to meet the expectations of the firm's ethical and environmental policy values of X and Y must satisfy the constraint x+y-5x-6y= 210. How many units of each type should firm buy in other to maximize total volume? What is the implication of a unit change in investment in capital and (or) Labour Economic Analysis?