Q4The output of a production process, Q, is given by the functionKLQ =K+ 2Lwhere K and L denote capital and labor.(a) Calculate the output when the capital and labor are 40 and 30 units, respectively.(b) Find the level of labor needed to produce 4 units of output when 10 units of capital are used.(c) Transpose this formula to express K in terms of Q and L.Q53The equations defining a simple model of the economy are:C = 0.75Y + 18I = 22where C, Y and I denote consumption, national income and planned investment,respectively.Use this model to complete the following table of values and hence draw an accurategraph of C + I plotted against Y on the interval 0 < Y< 200.100200C + IBy drawing a second line on the diagram, calculate the equilibrium level of national income.Use your graph to explain what happens to the equilibrium level of national incomewhen the marginal propensity to consume decreases with autonomous consumption fixed.

Q4 The output of a production process, Q, is given by the function KL K+ 2L where K and L denote capital and labor. (a) Calculate the output when the capital and labor are 40 and 30 units, respectively. (b) Find the level of labor needed to produce 4 units of output when 10 units of capital are used. (c) Transpose this formula to express K in terms of Q and L. 05

Q4 The output of a production process, Q, is given by the function KL K+ 2L where K and L denote capital and labor. (a) Calculate the output when the capital and labor are 40 and 30 units, respectively. (b) Find the level of labor needed to produce 4 units of output when 10 units of capital are used. (c) Transpose this formula to express K in terms of Q and L. 05

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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The production of a certain good in terms of the amount of labour invested L and the amount of capital invested K, is given by the production function Q = 5 L²/3 K ¹/3 At this moment 512 units of labour and 1 000 units of capital are invested daily. This means that at this moment 3200 units are produced daily. a) The company receives an order for 3200 units. Give an implicit equation for the combinations (L, K) resulting in a production of 3200 units. b) Determine K'(L) for L = 100 using implicit differentiation. Interpret your result in a sentence in the context of the word problem. c) Determine the following expression and interpret your result in a sentence in the context of the word problem: 100 K'(100) K d) Set up the graph of K as a function of L using a logarithmic scale on both axes. Interpret the slope in L = 100.
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The daily output at a factory is Q(K, L) = 144KL units, where K is the capital investment measured in units of $1000 and L is the size of the labor force measured in worker-hours. (a) Compute the daily output if the capital investment is $139,000 and the size of the labor force is 1025 worker-hours. (b) What will the output be if both the level of capital investment and the size of the labor force are cut in half?