2.4 Draw the isoquants and find the cost function corresponding to each of thefollowing production functions:Case A : q = ²2Case B : q=0121 + a₂%2Case C= q=a1²² +₂²²Case D : q = min21(23)01 01where q is output, z₁ and 22 are inputs. a1 and as are positive constants. [Hint:think about cases D and B first; make good use of the diagrams to help you findminimum cost.)1. Explain what the returns to scale are in each of the above cases using theproduction function and then the cost function. Hint: check the result onpage 25 to verify your answers/2. Discuss the elasticity of substitution and the conditional demand for inputsin each of the above cases.

We are given four different production functions, each with different forms. We are tasked…

Answered: 2.4 Draw the isoquants and find the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Q5The rate of change of the function f(x) =x + 2 /1 − 8xwith respect to x when x = 1. (i) The number of units Q of a particular commodity that will be produced with K thousand dollars of capital expenditure is modeled by Q(K) = 500 K^2/3. Suppose that capital expenditure varies with time in such a way that t months from nowthere will be K(t) thousand dollars of capital expenditure,whereK(t) =2t4 + 3t + 149 /t + 2 Required:(a) What will be the capital expenditure 3 months from now? How many units will be producedat this time? (b) At what rate will production be changing with respect to time 5 months from now?Will production be increasing or decreasing at this time?
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1. The following production function is used to produce wheat, q, from capi- tal, K, and labour, L: q = f(K, L) = «³K/3 + B³L/3 a) Describe the role of a and B in this production function. b) Derive the slope of an isoquant for this production function and in- terpret your result. Draw the isoquant in (K L) space, labeling where appropriate. The drawing does not need to be exact, but the curvature needs to be approximately correct. Explain why under- standing the curvature is so important. | c) Does this production function follow the "Law of Diminishing Marginal Returns"? Show your work and explain your answer.
uppose a Cobb-Douglas Production function is given by the following:P(L,K)=60L^0.8K^0.2where LL is units of labor, KK is units of capital, and P(L,K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $900 and each unit of capital costs $3,600. Further suppose a total of $900,000 is available to be invested in labor and capital (combined).A) How many units of labor and capital should be "purchased" to maximize production subject to your budgetary constraint?Units of labor, LL = Units of capital, KK = B) What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.)Max production = units
The table below forms part of production function analysis for Elegance Holdings Ltd. No. of workers Total Physical Average product Physical Product 0 1 3 5 7 8 11 12 14 Required: 0 12 30 54 90 100 115 115 110 Marginal Physical Product a) Compute: i. The Average Physical Product ii. The Marginal Physical Product b) Draw the curve that illustrates the three relationships. c) From the diagram that you have drawn in B above, prove the law of diminishing returns.
Q = a,H + a,L +a,H² +a¸L² +a‚HL , where a,>0 2. Q = aH " L, where a, a, y> 0 a) Derive the equation of the relevant Isoquant. b) Find out whether the production function is well behaved.
1. Assume a daily production function for a firm is Q= min(3L, 4K) a, If L = 100 and K = 100 what quantity is produced? Explain why. b. What would be the cost-minimizing labor and capital combination for this firm to produce Q = 1200? (show your work) Labor = Capital = At this level of production from part b (Q-1200), if the wage rate is: w- $30 and the rental rate of capital is: r= $100, what is the total cost of production? (show your calculations) C.
Please indicate which multiple choice awnser is correct for question 1.1)1.2)1.3)Please indicate it correctly as I have had this awnsered with different letters to the awnser I was told 1.1 - A firm trebles its inputs and discovers that its output rises by a factor of four. This is an example of;Select one or more:a. constant returns to scaleb. diminishing returns to a variable factor c. increasing returns to scaled. economies of scale1.2 - Diseconomies of scale are present when.... Select one or more:a. marginalcostsriseb. long run average costs rise as output rises c. totalcostsfallasoutputrisesd. total costs rise as output rises 1.3 - If the demand for a firm’s product is price inelastic, this implies that Select one or more: a. price changes have no impact on quantity demandedb. a fall in price of 3% will lead to a decline in quantity demanded of more than 3%c. a rise in price will raise total expenditure on the goodd. a 5% rise in price will result in a fall in quantity…
Jeff spends all of his money on housing (H) and other stuff (S) and has a diminishing marginal rate of substitution between housing and stuff. Jeff used to live and work in a small town where housing prices were relatively low. His company has decided to transfer him to a large city where housing prices are higher. (For simplicity, assume that all other prices are the same.) Using a diagram, explain to Jeff's company how to find the amount it needs to raise his salary to keep him just as well after the 2. transfer as he was before. Tridor
Can marginal utility be negative? Briefly explain with an example
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.
The following equations represent the long-run production functions for four different technologies, where capital and labor are both variable inputs. For each function, indicate whether it exhibits increasing, decreasing, or constant returns to scale. Clearly show your derivations. (Note that in parts a and c, the exponents are decimals.) f(L,K)= 8L²K4 b. f(L,K)= L+7K c. f(L,K)= L³K d. f(L,K)= 4L+K? а. с.

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