1) A firm uses two inputs K and L of capital and Labor respectively, toproduce a single output Q according to the specific type of productionfunction:Q= F (K, L) =k°L".a,b >0The prices of capital and labor are rand w, respectively.(1) Find the cost minimizing input of capital (K)(1i) Find the cost minimizing input of Labor (L)Note: These are also called the demand functions of K and L.(li) Write down the cost function of the firm.

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1) A firm uses two inputs K and Lof capital and Labor respectively, to produce a single output Q according to the specific type of production function: Q=F (K, L) =*°L°, a,b>0 The prices of capital and labor are r and w, respectively. ) Find the cost minimizing input of capital (K) (1) Find the cost minimizing input of Labor (L) Note: These are also called the demand functions of K and L. (i) Write down the cost function of the firm.

1) A firm uses two inputs K and Lof capital and Labor respectively, to produce a single output Q according to the specific type of production function: Q=F (K, L) =*°L°, a,b>0 The prices of capital and labor are r and w, respectively. ) Find the cost minimizing input of capital (K) (1) Find the cost minimizing input of Labor (L) Note: These are also called the demand functions of K and L. (i) Write down the cost function of the firm.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.
2. A firm has a production function given by the following table: Units of Labor 1 2 3 4 5 K=1 3 8 12 15 17 K=2 10 15 19 22 24 K=3 16 21 25 28 30 K=4 20 25 28 30 31 (1) Suppose that K is fixed at 2. Does this production function exhibit diminishing marginal returns? (ii) Does this production function exhibit constant returns to scale for all values of K and L?
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A firm's production function takes the form: Q(L, K) = min{2L, 3K}, where Q represents output and L and K represent labour and capital, respectively and where w and r give the prices of labour and capital. Assuming no other costs, what would be the marginal cost if the firm increased output by 1 unit? O O MC = Q [ 12/2₁ = Q ( + 1/2 + 1/2 ) MC = W 3r 3w+2r 3w+2r + O MC=3w+2r O W r = 21/1/2+1/1/3/2 O MC =2w+3r MC=1/2
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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.
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