Help (a)Consider the following data on the fictional countries of Sylvania and Freedonia.The production function is y = Akah¹-a, where a = 0.5.Sylvania FreedoniaOutput per Worker, y100200Physical Capital per Worker, k100100Human Capital per Worker, h2564(b) Calculate the level of productivity, A, in each country.(c)(d)Calculate the countries' relative levels of output if all differences in output were theresult of productivity.Calculate the countries' relative levels of output if all differences in output were theresult of factor accumulation.

a) To calculate the level of productivity, A, in each country, we can use the production function…

Answered: (a) Consider the following data on the…

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 3E

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*0.65 0.35 where x is the amount of labor and y is the amount of capital. The productivity of a country is given by f(x,y) = 100x (a) Compute the marginal productivities of labor and capital when x = 300 and y = 500. (b) Use part (a) to determine the approximate effect on productivity of increasing capital from 500 to 502 units, while keeping labor fixed at 300 units. (c) What would be the approximate effect of decreasing labor from 300 to 298.5 units while keeping capital fixed at 500 units? (a) The marginal productivity of labor is (Do not round until the final answer. Then round to two decimal places as needed.) The marginal productivity of capital is (Do not round until the final answer. Then round to two decimal places as needed.) (b) When capital is increased from 500 to 502 units, the approximate change in productivity is (Do not round until the final answer. Then round to two decimal places as needed.) (c) When labor is decreased from 300 to 298.5 units, the approximate change…
Consider an economy that exhibits both population growth (L grows at rate n) and technological progress (A grows at rate a) described by the production function, Y = F(K,AL) = Kª(AL)¹-α| Here K is capital and Y is output. (a) Show that this production function exhibits constant returns to scale. What is the per-effective-worker production function? (c) Find expressions for the steady-state capital-output ratio, capital stock per effective worker, and output per effective worker, as a function of the saving rate (s), the depreciation rate (8), the population growth rate (n), the rate of technological progress (a), and the coefficient a. (You may assume the condition that capital per effective worker evolves according to Ak = sf (k) − (a +n+8)k.) (d) Show that at the Golden Rule steady state the saving rate for this economy is equal to the parameter a.
Assume the following production function for maize: Q=3K^1.2 L^0.5, where Q is the number of bags of maize produced, K is the units of capital used and L the units of the labour employed. (a) Derive the MRTS of K and L. (b) Estimate the factor intensity of the production function and interpret results. (c) Is the above production function characterized by decreasing returns of scale? Explain
Assume the rate of technological progress is constant in a SSGM with Cobb- Douglas production function. Show that a steady-state cannot be identifiede if the technological progress is capital augmented, i.e. F(K, L) = [A(t)K(t)]*L(t)'_ª, where A(t) is the efficiency term growinge with a constant rate g.t
1. Consider an economy where the production function is Y = K0.5 (LE)0.5 The depreciation rate is = 0.04, the savings rate is s = 0.2, the popula- tion growth rate is n = 0.03 and technology growth rate is g = 0.03. (a) What is the 'per effective worker' production function? (b) Find the steady state levels of capital per effective worker (k*), in- come per effective worker (y*), investment per effective worker (¿*) and consumption per effective worker (c"). (c) Find the golden rule levels of capital per effective worker (kg), income per effective worker (y), investment per effective worker (it) and consumption per effective worker (c2). Also find sg, that is the level of the savings rate that would lead the economy to the golden rule steady state. (d) Suppose the government pursues policies that change the savings rate from s = 0.2 to sg. What is the immediate effect on income per effective worker and consumption per effective worker? What is the long run effect on income per…
Some less-developed nations are unable to devote resources to various research and development projects. Attempting to increase their economic growth, sometimes they acquire pharmaceutical or technological goods and reverse engineer them to determine how they’re made, then sell them in domestic markets. Is it ethical and/or necessary to produce and sell a product without having developed it and not having a patent for the product? What could be the short run and long run consequences of such an action?
For a production function q= f(K, L) = K^1/3 L^1/3 and factor prices w=8 and r=1, answer the following questions: (a) Explain what returns to scale mean and its implication for the cost function. What returns to scale does this production function exhibit? (b) optimal mix and equation of the expansion path. What does it show? (c) Minimized cost function for the technology. (d) Why are the short-run cost curves different from the long-run cost curves? Your answer must include the terms expansion path and optimal input mix.
The daily output at a factory is Q(K, L) = 144KL units, where K is the capital investment measured in units of $1000 and L is the size of the labor force measured in worker-hours. (a) Compute the daily output if the capital investment is $139,000 and the size of the labor force is 1025 worker-hours. (b) What will the output be if both the level of capital investment and the size of the labor force are cut in half?
In our one country model of technology growth, y = A(1- yA). Suppose that the country temporarily raises its level of yA. (a) Draw two graphs, one for y and one for A, showing how the time paths of output per worker (y) and productivity (A) will compare under this scenario with what would have happened if there had been no change in yA.
Problem 1: Solow On a new sheet of paper show the work for each question. Suppose the economy of an island behaves as the Solow model, version 1.0 (constant population). The production function is Cobb-Douglas (with constant returns to scale) and the exponent on capital is 0.4. Further, the productivity parameter is 50 (A), the depreciation rate is 10% (d), the savings (investment) rate is 20% (s), and the labor force (L) is equal to 50 million (and constant over time).
Problem 1: Solow On a new sheet of paper show the work for each question. Suppose the economy of an island behaves as the Solow model, version 1.0 (constant population). The production function is Cobb-Douglas (with constant returns to scale) and the exponent on capital is 0.4. Further, the productivity parameter is 50 (A), the depreciation rate is 10% (d), the savings (investment) rate is 20% (s), and the labor force (L) is equal to 50 million (and constant over time). Suppose in year 2020 the economy is in a steady state. Compute the 2020 values for income per worker (Y/L) and the wage (w). Recall that the wage is given by the MPL. Pick the best choice from the options below. Per-worker income is higher than 520 and lower than 610. The wage coincides with per-worker income. Per-worker income is higher than 900 and lower than 1,150. The wage is between 610 and 660. Per-worker income is higher than 550 and lower than 820. The wage is between 420 and 490. Per-worker income is higher…
The table attached reports per capita GDP and capital per person in the year 2017 for 10 countries. Your task is to fill in the missing columns of the table.(a) Given the values in columns 1 and 2, fill in columns 3 and 4. That is, compute per capita GDP and capital per person relative to the U.S. values.(b) In column 5, use the production model (with a capital exponent of 1/3) to compute predicted per capita GDP for each country relative to the United States, assuming there are no TFP differences.(c) In column 6, compute the level of TFP for each country that is needed to match up the model and the data.(d) Comment on the general results you find.

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