Population Growth and Technological Progress – Work It OutPLEASE WRITE ANSWERS CLEARLYAn economy has a Cobb-Douglas production function:Y = K“(LE)'-aThe economy has a capital share of 0.30, a saving rate of 42 percent, a depreciation rate of 4.00 percent, a rate of populationgrowth of 5.25 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state.b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital.k* =y* =marginal product of capital =

Marginal Product of Capital is defined as the additional output which results from adding one extra…

Answered: An economy has a Cobb–Douglas…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

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Consider the following Cobb-Douglas production function: Y = 10L04K04. Suppose that the price of labor is w = 20 and the price of capital if r = 40. a- Derive the total cost curve for this production function. b- Derive the marginal cost curve for this production function. c- Plot the marginal and total cost curves for q = 1,2,3,4,5. What does it tell you about economies of scale for the production function? d- Suppose that the wage rate went up from 20 to 30. What would happen to the total wage bill relative to total costs, wL ;? What would happen to total costs? wL+rk*
If the production function is Q = 30 + 22L + 30K, what's the most you can produce with 5 workers (L) and 7 unit of capital (K)? Enter as a value.
Consider the production function q = ((K^α)+(L^α))^β. For this function to have diminishing marginal productivities and increasing returns to scale, it must be the case that: a. α>1 & αβ>1; b. α>1 & αβ1; d. α
In the following production function: f(x1, x2) = Ax1α1 x2α2 , where A, α1, α2 > 0. What is the marginal product of input 1?
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A Firm's Optimization with CES Production Function The Constant Elasticity of Substitution (CES) production function is a flexible way to describe how a firm combines capital and labor to produce output, allowing for different levels of substitutability between the two inputs. The elasticity of substitution, denoted by σ, measures how easily the firm can substitute capital for labor (or vice versa) while maintaining the same output level. The parameter p is related to the elasticity of substitution by the formula σ = 1/(1 - p). Now, let's consider a firm that operates for two periods (t and t + 1) and produces output according to the CES production function: F(Kt, Nt) = [aK{ + (1 − a)N]¹º 0
Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a) Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve. (b) At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point? (c) Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0? (d) Does this production function exhibit constant, increasing or decreasing returns to scale?
The equation below is a production function, Q = (200)L + (100)K – (0.2)L2 – (0.1)K2 , where Q is output, L is labor and K is capital. What is the Marginal Product of Labor of this function?
A firm faces a production function with inputs capital (K) and labor (L): F(K, L) = K¹/² L¹/4 The amount of capital used for production is determined at the beginning of the year. The prices of K and L are v and w respectively.
Company Z has the following data corresponding to the production function. Where (L) is the amount of the labor factor and (K) capital. Q=K0.4 L 0.6 a) Calculate the amount of production, applying the production function for each of the respective values of K and L. K L Q 10 80 30 160 50 320 70 640 90 1200 a) Graph the amount of production obtained on the Y axis, and with the labor input on the Х аxis b) Draw isoquant lines for each level of production, placing capital on the Y axis and labor on the X axis, to better appreciate the displacement.
Question # 1: Majeda wrote the following answer on her microeconomics examination: “Virtually every production function exhibit diminishing returns to scale because my professor said that all inputs have diminishing marginal productivities. So, when all inputs are doubled, output must be less than double." How would you grade Majeda's answer? Question # 2: Suppose a firm had a production function with linear isoquants, implying that its two inputs were perfect substitutes for each other. What would determine the firm's expansion path in this case? For the opposite case of a fixed-portions production function, what would the firm's expansion path be? Question # 3: Suppose that a firm's production function is q = 30√L. In the short run, where there are fixed costs of $2,200, and labor is the variable input whose cost is $6,300 per units. What is the total cost of producing 20 units of output?
In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q = f(L, K), where is output, L is workers, and K is the fixed number of units of capital. Given a specific equation for production: or, when K = 29, Calculate the q = 8LK+ 5L² q = (8L × 29) + 5L² X - Average Product = 3 (13) ₁³. 102 and enter the values in the table to the right. (Round your answers to the nearest integer.) E Labor 624 0 6 8 10 12 Output or Product 0 481 987 1,500 2,005 2487 2,928 Production Marginal Product -- 241 253 257 253 241 221 Average Product -- 241 247 251 249

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An economy has a Cobb–Douglas production function: Y = K“(LE)1-a