19.2 (0) Suppose X₁ and x2 are used in fixed proportions and f(x₁,x2) = min{x₁,x₂).(a) Suppose that x₁ < x₂. The marginal product for x, is andfor small(increases, remains constant, decreases),K6 TECHNOLOGY(Ch. 19)increases in x₁. For x₂ the marginal product is, and (increases, remainsconstant, decreases).for small increases in x₂. Thetechnical rate of substitution between x₂ and x₁ istechnologydemonstrates (increasing, constant,Thisdecreasing)returns to scale.(b) Suppose that f(xx) = min(x,x) and x₁ = x₂= 20. What is themarginal product of a small increase in x₁? What is the marginal productof a small increase in x₂? The marginal product of x, will (increase,if the amount of x2 is increaseddecrease, stay constant)by a little bit.Douglar and

The technical rate of substitution (TRS), also known as the marginal rate of technical substitution…

19.2 (0) Suppose x, and x2 are used in fixed proportions and f(x,x) = min(x,x). (a) Suppose that x₁ < x₂. The marginal product for x, is (increases, remains constant, decreases). 6 TECHNOLOGY (Ch. 19) increases in x₁. For x₂ the marginal product is constant, decreases). technical rate of substitution between x2 and x₁ is technology demonstrates (increasing, and for small and (increases, remains for small increases in x₂. The constant, This decreasing) returns to scale. (b) Suppose that f(xx) = min(xLxz) and x₁ = x₂= 20. What is the marginal product of a small increase in x₁? What is the marginal product

19.2 (0) Suppose x, and x2 are used in fixed proportions and f(x,x) = min(x,x). (a) Suppose that x₁ < x₂. The marginal product for x, is (increases, remains constant, decreases). 6 TECHNOLOGY (Ch. 19) increases in x₁. For x₂ the marginal product is constant, decreases). technical rate of substitution between x2 and x₁ is technology demonstrates (increasing, and for small and (increases, remains for small increases in x₂. The constant, This decreasing) returns to scale. (b) Suppose that f(xx) = min(xLxz) and x₁ = x₂= 20. What is the marginal product of a small increase in x₁? What is the marginal product

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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13. Suppose you have a production technology given by f(x1, x2) = min{2x₁, x2} and you are producing at the point where x₁ = 10 and x₂ = 20. (a) Explain in words what we mean (generally) by the ‘marginal product' of an input in production. (b) For the production technology in this question and the initial point x₁ = 10 and x2 = 20, what is the marginal product of a small increase in input 1? (c) Suppose input 2 increases and you are now at the initial point x₁ = 10 and x2 = 30. Relative to your answer in part (b), does the marginal product of input 1 decrease, increase, or stay constant? Explain briefly.
***QUESTION HAS FOUR PARTS - ALL PARTS MUST BE ANSWERED TOGETHER AS THEY ARE DEPENDENT ON EACH OTHER*** 1. A farmer raises apples using land (K) and labor (L), and has an output of ? (?,?) = ? 0.5 ? 0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor? d. In the long run, the farmer can change both his amount of land and his amount of labor. Suppose…
a firm that has the following production function: √（KL^2）Where, K and L are the units of capital and labour used in the production process respectively. a)Calculate the marginal products of labour and capital. b)What is the value of marginal rate of technical substitution when 4 units of capital and 3 units of labour are used?
Refer to the graph below: y2 The graph above illustrates a production set of a firm. (a) Which assumption(s) do(es) the production set violates? Explain. (b) Suppose the firm decided to scale all inputs up or down by some amount t > 0. What will happen to the level of output?
Production Total Product Total Fixed Cost Total variable cost Total Cost Average fixed cost Average variable cost Average Total Cost Marginal Cost 0 0 1 25 2 45 3 60 4 70 5 85 6 105 7 135 8 180 9 240 10 315 Assume that fixed costs are $50, labor is the only variable input and its costs are reflected completely in the costs above. Complete the table Graph AFC, AVC, ATC, and MC Explain how increasing returns and decreasing returns are depicted in your graph If the labor input increased by $10 at every unit of production, what would be the effect on your graphs?
A firm is currently producing 500 units of output daily by employing 60 units of labor daily at a price of $10 per unit and 30 units of capital daily at a price of $20 per unit. The marginal product of the last unit of labor employed is 3, and the last unit of capital employed is 5. a. Given the above information, what does the firm's marginal rate of technical substitution, MRTSL,K, equal? b. Indicate on the following diagram some point labeled A that is consistent with the information given in the question.
Briefly explain and graphically illustrate the property of diminishing marginal rate of technical substitution and its relation to marginal productivities.
Consider the isoquant for gelato production as graphed below. Use the graph to answer question 27. Inagedhents A 142 100 2000 Liters of Gelato 20 26 Labor (Emplayges) 27. What is the marginal rate of technical substitution between points A and B? 42 (а) +- 42 (b) 6 (c) 42 (d) It is not possible to determine from this graph.
31) Which of the following statements is true? A) The average product of labor is at its maximum when the average product of labor equals the marginal product of labor. B) The average product of labor is at its minimum when the average product of labor equals the marginal product of labor. C) The average product of labor tells us how much output changes as the quantity of workers hired changes. D) Whenever the marginal product of labor is greater than the average product of labor the average product of labor must be decreasing. 32) Which of the following explains why the marginal cost curve has a U shape? A) Initially, the marginal product of labor rises, then falls. B) Initially, the average product of labor falls, then rises. C) Initially, the marginal product of labor falls, then rises. D) Initially, the average cost of production rises, then falls. 33) If marginal cost is above the average variable cost, then average variable cost is decreasing. A) TRUE B) FALSE
A certain production process employs two inputs--labor (L) and raw materials (R). Output (Q) is a function of these two inputs and is given by the following relationship: Q = 6L² R? - .10L R3 Assume that raw materials (input R) are fixed at 10 units. (a) Determine the total product function (TPL) for input L. (b) Determine the marginal product function for input L. (c) Determine the average product function for input L. (d) Find the number of units of input L that maximizes the total product function. (e) Find the number of units of input L that maximizes the marginal product function. (f) Find the number of units of input L that maximizes the average product function. (8) Determine the boundaries for the three stages of production. A.600L^2-10000L^3 B. 1200L-30000L^2 C. 600L-1000OL^2
***PLEASE NOTE - An answer is NOT needed for parts A, B and C; these are included to assist with answering part D. Only an answer for part D is required, but it is derived from the previous answers*** Given: A farmer raises peaches using land (K) and labor (L), and has an output of ?(?,?)= ?0.5?0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor?…
A certain production process employs two inputs--labor (L) and raw materials (R). Output (Q) is a function of these two inputs and is given by the following relationship: Q = 6L² R? – .10L³ R³ Assume that raw materials (input R) are fixed at 10 units. (a) Determine the total product function (TPL) for input L. Determine the marginal product function for input L. (b) (c) Determine the average product function for input L. (d) Find the number of units of input L that maximizes the total product function. (e) Find the number of units of input L that maximizes the marginal product function. Find the number of units of input L that maximizes the average product (f) function. (g) Determine the boundaries for the three stages of production.