Let c(x) be the cost of producing a product of x units. Given that c(x) follows the experience cost curve, c(x)= k(1 – b) xb-1 where k and b are constants and 0 < b < 1. Show that c(x) is a decreasing function, in this case. production costs show a downward trend with an increase in the number of products produced! Is this function a convex function? Explain!

Let c(x) be the cost of producing a product of x units. Given that c(x) follows the experience cost curve, c(x)= k(1 – b) xb-1 where k and b are constants and 0 < b < 1. Show that c(x) is a decreasing function, in this case. production costs show a downward trend with an increase in the number of products produced! Is this function a convex function? Explain!

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Juan Valdez owns a coffee farm in Colombia. His production function is: f(x1,x2)=(x1−1)^0.25 x2^0.5 Assume the price of input 1 is r and the price of input 2 is w. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm?
Consider the following production function: f (A, B) = gamma multiply A^alpha multiply B^Beta. where A and B are the inputs and alpha, Beta, gamma are in the set (0,1). Let wA and wB the price of the two inputs. Assume wA, wB > 0. Is the production function separable?Does the production function exhibit constant returns of scale?Compute the cost function and the conditional input demand function.How do these three functions react to a change in wA? Suppose the price of both inputs double, what happens to the conditional input demand function? And to the cost function? Suppose the desired level of output double, what happens to the conditional input demand function? And to the cost function?…
Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm has the production function Q(K, L)=KxL, where Q is the hours of edited footage. The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units of output at the lowest possible cost.a) Find the marginal product of each input.b) Determine whether the production function exhibits diminishing marginal product to each input.c) Find the marginal rate of technical substitution(MRTSLK)d) How does MRTSLK change as more L, is used holding output constant.e) Find the least costly combination of labor and capital to produce 3000 units
A firm’s production is represented by the following function: Q = L1/4 K3/4 . The rental rate of capital (r) is $40 and the wage rate (w) is $12.a. For a given level of output, what should be the ratio of capital to labor in order to minimize costs?b. How much capital and labor should be used to produce 400 units of output? What is the total cost?c. What is the short run total cost if output is decreased to 300 units?d. How would the capital labor choice and total cost change in the long run?e. Would the firm prefer to relocate if input prices are r = 60 and w = 8 at an alternativelocation assuming relocation is costless?
Consider a firm that produces widgets according to the following Cobb-Douglas production function: Q = A * L^α * K^β where: Q is the quantity of output, L is the quantity of labor, K is the quantity of capital, A is a scale parameter (total factor productivity), α and β are the output elasticities of labor and capital respectively. Given that A = 1, α = 0.6, β = 0.4, L = 16 and K = 9, a) Calculate the quantity of output Q. b) If the firm increases the quantity of labor (L) to 20 while keeping the quantity of capital (K) constant, what will be the new quantity of output?
Consider the production function q=√L+8K^(3). Starting from the input combination (3,6), does the production function exhibit increasing, constant or decreasing returns to scale if inputs double?
Suppose that the production function for Hannah and Sam's home remodeling business is Q=f(L,K) Q=1040.2K0.3 Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $2,000 per week. a. What is the least-cost input combination for remodeling 100 square feet each week? Instructions: Round your answers to 2 decimal places. units of labor and units of capital. b. What is the total cost? Instructions: Round your answer to 2 decimal places.
Consider the following production function when K is fixed. (This is a description of the figure: it shows a two-axis graph; in the horizontal axis we measure labor and in the vertical axis we measure meals; the graph of the production function is a line that intersects the vertical axis at a positive amount; this graph is a line with positive slope and passes through the point (4,300)). Can we say that the production function satisfies the law of decreasing marginal returns of labor?True False
The figure shows the production function of a farmer who produces grain by working certain hours each day. Which of the following statements is correct about this production function? a. The slope of the production function represents the marginal rate of substitution. b. The ceteris paribus assumption means that the farmer becomes more productive as he works more hours. c. A rightward movement from B along the production function implies that the farmer has better technology. d. This production function exhibits economies of scale. e. A technological improvement would shift up the production function
The Cobb-Douglas production function for a particular product is N(x,y) = 80x0.6.0.4, where x is the number of units of labor and y is the number of units of capital required to produce N(x, y) units of the product. Each unit of labor costs $40 and each unit of capital costs $60. Answer the questions (A) and (B) below. (A) If $150,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production, and find the maximum production. (B) Find the marginal productivity of money in this case, and estimate the increase in production if an additional $50,000 is budgeted for the production of the product. C (A) If $150,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production, and find the maximum production. Production will be maximized when using units of labor and units of capital.
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.. +
Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function. S = 20L0.30c0.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 60,000 tons of steel at minimum cost. Min s.t. = 60,000 L, C 20 (b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L> 0 and C > 0. Round your answers to the nearest integer.) $ at (L, C) =