Suppose the economy of Utopia has a labor force of 600 workers, 100 units of capital and 400 hectares of land. It produces manufactured goods (M) which use labor (LM) and capital (K) in production and agricultural goods (A) which use labor (LA) and land (T) in production. The production functions are given by:
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- Suppose the production function is given by Q = 5K+2L. What is the marginal product of capital when 5 units of capital and 10 units of labor are employed?Economics: Industrial Economics Question: 1 A firm produces output according to the following production function: q = 10 K^1/4 L^1/4 The price of capital is r = 9 and the price of labor is w = 25 and there is a set-up cost F = 90 that the firm only pays if it decides to produce in the market. If the firm wants to produce 'q' units of output, solve the cost minimization problem. Obtain total cost C* (as a function of output level q). Now assume that the firm operates under monopoly and the inverse demand function is p = 115 - 2 q Use the solution to the cost minimization problem to solve the profit maximization problem of this firm. Determine this firm's price p*. Please Show your Work. a. 55 b. 75 c. 85 d. 65 Question: 2 A firm produces output according to the following production function: q = 10 K^1/4 L^1/4 The price of capital is r = 9 and the price of labor is w = 25 and there is a set-up cost F = 90 that the firm only pays if it decides to produce in the market. If the firm…Suppose that the economy's production function is given by Y=K²N¹-a where Y is output, K is capital, and N is labor. Assume that a = 1/3. The production function transformed into output per worker is (Property format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with N character.)
- A farmer has 1 acre of land. If he uses X pounds of fertilizer he can harvest √x tons of wheat. What is his production function if he has A acres of land and can just replicate the same production process on each piece of land? XXX A * A VXA √XAHannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function Q=F(L,K) Q=10L^0.25 K^0.25 where L is their number of workers and K is units of capital. The wage rate is $500 per week and a unit of capital costs $500 per week. Suppose that when initially producing 10 square feet a week, they use 1 unit of capital.a. What is their short-run cost of remodeling 80 square feet per week? Instructions: Round your answer to the nearest whole number. $ b. What is their short-run average cost of remodeling 80 square feet per week? Instructions: Round your answer to the nearest whole number. $ c. What is their long-run cost of remodeling 80 square feet per week? Instructions: Round your answer to the nearest whole number. $ d. What is their long-run average cost of remodeling 80 square feet per week? Instructions: Round your answer…Consider the following production functions and match them to the word that describes their returns to scale. Production function A: F(L,K) = K²L Production function B: F(L,K) = 25K + 10L Production function C: F(L,K) = (KL)¹2 Production function D: F(L,K) = 5L² + L¹/2K1/2 Production Function A✔ Choose... Decreasing Production Function B Constant Production Function C Increasing Production Function D Choose.. +
- QUESTION THREE: PRODUCER THEORY 1. Suppose the production function for automobiles is given by q = kl - 0.8k² - 0.21² where q represents the annual quantity of bicycles produced, k represents annual capital input, and I represents annual labor input. a) Suppose k=10; graph the total and average productivity of labor curves. At what level of labor input does this average productivity reach a maximum? How many cars are produced at that point? b) Again, assuming k=10, graph the MP curve. At what level of labor input does MP₁ = 0 c) Suppose capital inputs were increased to k-20. How would your answer to parts (a) and (b) change? d) Does the production of automobiles exhibit constant, increasing, or decreasing returns to scale? 2. Supposing that the firm in (1) is a competitive firm and its production function is y = 10 + (x - 1,000)¹/3. The price of the input x is w = 1. (a) Show that the firm's total cost curve is C(y) = 1,000 + (-10)³. (b) Show that the minimum of the marginal cost curve…Suppose a firm is producing computer monitors utilizing the following technology: Q=F(K,L)=L1/3K2/3 Q – weekly output L – labor hours K – hours of capital use Would the firm with the above production function be able to produce monitors using only capital (no labor)? Explain.Suppose the production function is given by G = 10K - 8L. What is the average product of capital when 2 units of capital and 10 units of labor are employed?
- Q1: Usher Dash is president of Dash Manufacturing, a producer of Go-Kart tires. Dash makes 870,000 tires per day with the following resources: Labor 1670 hours per day @ 225 per hour Raw Material 900,000 pounds per day @ Rs.10 per pound Energy Rs.87,000 per day Capital Rs.560,000 per day a) What is the labor productivity per labor hour for these tires? b) What is the multifactor productivity for these tires? c) What is the percentage change in multifactor productivity if Upton can reduce the energy bill by Rs.13,000 per day without cutting production or changing any other input? What is the capital productivity per tire per rupee?In economics and econometrics, the Cobb-Douglas production function is a particular functional form of ne production function, widely used to represent the technological relationship between the amounts of two r more inputs (particularly physical capital and labor) and the amount of output that can be produced by nose inputs. The function they used to model production is defined by, P(L, K) = 6LªK!-a where P is the total production (the monetary value of all goods produced in a year), L is the amount f labor (the total number of person-hours worked in a year), and K is the amount of capital invested (the onetary worth of all machinery, equipment, and buildings). Its domain is {(L, k)|L > 0, K > 0} because L nd K represent labor and capital and are therefore never negative. Show that the Cobb-Douglas production function can be written as P P(L, K) = 6LªK1-a → In K L In b+ a ln KThe Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L, C) = c₂LC1C²2 C2 are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume co 5, C₁ = 0.25, and c2₂ 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $90,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. = = where co, C₁, and Max s.t. L, C ≥ 0 A ≤ 90,000 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in dollars)? Hint: Put bound constraints on the variables based on the budget constraint. Use L ≤ 3,000 and C ≤ 1,000 and use the Multistart option as described in Appendix 8.1. (Round your answers to the nearest integer when…