2) Assume a firm has the following production function 4 = K³L%¸ Assume w = 2, v = 16 and that K = 27 in the short run Further assume the fim faces a market price of 32. %3D a) What is the firm's level of production and labor that can maximize the profit in the short run? b) If you were their economic consultant, what would you advise them to do regarding short run production and future adjustments to K and L? Explain

2) Assume a firm has the following production function 4 = K³L%¸ Assume w = 2, v = 16 and that K = 27 in the short run Further assume the fim faces a market price of 32. %3D a) What is the firm's level of production and labor that can maximize the profit in the short run? b) If you were their economic consultant, what would you advise them to do regarding short run production and future adjustments to K and L? Explain

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Accounting and Economic Profit analysis

One comes across the concept of Profits in the context of business and in analyzing the results of business activity. Profits of a business can be accounting profits, and they can also be economic profits. So how does one understand the concept of accounting versus economic profits?

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2) Assume a firm has the following production function: 1 = K³L3¸ Assume
w= 2, v = 16 and that K = 27 in the short run Further assume the firm faces a market
price of 32.
a) What is the firm's level of production and labor that can maximize the profit in the
short run?
b) If you were their economic consultant, what would you advise them to do regarding
short run production and future adjustments to K and L? Explain

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4. Find the cost function and the conditional demands for inputs associated to the CES production function f(r1, #2) = A(ar{ + (1 – a)a)/e, where A, 8 > 0, 0 < a < 1, and 0#p< 1.
Find the elasticity of scale and the elasticity of substitution for the CES production function: 1 1 f(x₁, x₂) = (x³ + x2)³. Solution: We first calculate the marginal products: 2 fx₁ = 3 + = x1fx1 -+ 2 2 10 - ² ( x² + x ) ( + x^²) = ( + + + + ² ) 15 ²0 x² -2/3 x₂ + x2fxz Elasticity of scale = _1₁_+_*__*(+)´<°¸«d«)*;»_ f(x1, f(x1, ‹2)² = -2/3 r2/3 = TRS = t (where TRS = =t). ⇒ r = t³/² ⇒ ln(r) = ln (t) and o = -2/3 dln (r) dln (t) To get elasticity of substitution, we first need TRS and denote r = 1 x3 X1 TMS - F (+4+2)0 = fx₁ fx₂ 2 1 + x²) x₂² MIN x2 3 -2/3 (x² -2/3 2 2/3 2/3 x1 -2/3 = r²/3 x¹/3 + 1/3 = 1.
Kris wants to open a BBQ restaraunt. He has signed a 12- month lease at $6,000 per month. The lease enabled him to rent a restaraunt with all the equipment he needs to make BBQ; therefore, K equals 1. Kris must pay his workers a monthly salary of $2,400 each. His production function is q = 100L1/2K1/2 where q is the quantity of BBQ prepared per month in pounds, L is the number of workers employed per month, and K is the quantity of capital employed, and, as previously indicated, K is assumed to equal 1. What does Kris's monthly total cost expressed as a function of quantity equal?
In workout problem 20.2, the production function is given by fx) = 4x/2, If the price of the commodity produced is $100 per unit and the cost of the input is $45 per unit, how much profit will the firm make if it maximize profits? %3D O $447.44 $442.44 $1,781.78 $873.89 $888.89
BJO Ⓒ4 f(X₁, X₂) = (x₁² + X₂²) & 0
.(a) A firm has production function q(k,l) = k'/³1²/3, where k denotes the capital used and I denotes the labour employed. Suppose that each unit of capital costs v dollars and each unit of labour costs w dollars, so that the capital and labour costs are vk + wl. Use the Lagrange multiplier method to determine the values of k and I that minimise the cost of producing Q units of the firm's good. Find the corresponding minimised value, C, of this cost and the value, X*, of the Lagrange multiplier corresponding to the optimising values of k and l. Show that d* =
6
1) Assume the production process can be represented by the following production function: Q=4K¹/²¹/2 We are operating in the short-run and thus K is fixed. We currently have use of 16 units of K. Note that the wage is $200 per worker, the rental rate of K is $150 per unit, and our output sells for $100 per unit. a) Write an expression for the MPL in the short-run:
Given the following data on input and output levels. Suppose the output price is $5 and input price is $10. Find the values of AVP and MVP when X = 4: X 0 2 4 6 8 10 12 Y 0 100 250 450 600 700 750 $312.50 and $375 $20 and $375 $265.50 and $475 $20 and $750
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The production function is given by Q=10L+2K. The wage for labor is $20 dollar per unit and price for capital is $5 per unit. The optimal bundle (L, K) to minimize cost is: (0, Q/2) (Q/20, Q/4) (Q/15, Q/3) (Q/10, 0)
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