Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Question
Chapter 17, Problem 17.4P
a)
To determine
To find:No profit condition in
b)
To determine
To know:Price of u-year old tree.
c)
To determine
To know:Value of woodlot.
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It’s mathematic for economics, and the questions should solve by the one of these
partial derivatives, Lagrange multipliers, first order differential equations.
Q2. A firm's production function is Q = 9LZ+1)/10KY+1)/10
%3D
• Find out MPL and MPK.
• Find out APL when K=16 L= 64.
An electronics plant’s production function is Q = 5LK, where Q is its output rate, L is the amount of labor it uses per period of time and K is the amount of capital it uses per period of time. The Price of labor is $1 per unit of labor and the price of capital is $2 per unit of capital.
a) What is the optimal combination of inputs the plant should use to produce 1000 units of output per period?
b) Suppose that the price of labor increases to $2 per unit. What effect will this have on optimal L and K to produce Q=1000?
c) Is this plant subject to decreasing returns to scale? Why or why not?
Chapter 17 Solutions
Microeconomic Theory
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- Is this change labor saving, capital saving, or neutral?arrow_forwardExercise 3 3.1 Consider the following production function: F(K,L) = K0.3L0.7 State if this function exhibits constant, increasing or decreasing returns to scale. 3.2 Consider the following production funetion: F(K,L) = K0.5L0.8 State if this function exhibits constant, increasing or decreasing returns to scale. 3.3 Consider the following production function: F(K, L) = K°L Find out what relation should exist between a and b in order for this function to exhibit constant returns to scale. 3.4 Constant returns to scale is an assumption that fits the reality most of the times. But it does not always hold. Make an example of a firm or a type of business in the real world that exhibits increasing or decreasing returns to scalearrow_forwardPlease find the attached photo. It’s mathematic for economics, and the questions should solve by the one of these partial derivatives, Lagrange multipliers, first order differential equations.arrow_forward
- What are the steps to solve for K in terms of L. Given a production function of Q = 2KL, and Q is 16, how do i solve and what are the steps to solve for K in terms of L. What if Q is 32? 64? Just algebra not calculus please.arrow_forwardThe Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L, C) = c₂LC1C²2 C2 are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume co 5, C₁ = 0.25, and c2₂ 0.75. Assume each unit of labor costs $25 and each unit of capital costs $75. With $90,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. = = where co, C₁, and Max s.t. L, C ≥ 0 A ≤ 90,000 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in dollars)? Hint: Put bound constraints on the variables based on the budget constraint. Use L ≤ 3,000 and C ≤ 1,000 and use the Multistart option as described in Appendix 8.1. (Round your answers to the nearest integer when…arrow_forwardIf a firm's production function is given by Q = 700Le-0.02L , %3D find the value of L that maximizes output.arrow_forward
- Suppose the production function for widgets is given by q=kl -0.8k²-0.21² where q represents the annual quantity of widgets produced, k represents annual capital input, and I represents annual labor input. Suppose k = 10; at what level of labor input does this average productivity reach maximum? (please put your answer in numerical values with no comma or decimal place). How many widgets are produced at that point? (please put your answer in numerical values with no comma or decimal place). If k = 10, at what level of labor input does MPL = 0? Suppose capital inputs were increased to k = 20, at what level of labor input does this average productivity reach maximum? widgets are produced at that point? (please put your answer in numerical values with no comma or decimal place). If k = 20, at what level of labor input does MPL = 0? answer in numerical values with no comma or decimal place). Does the widget production function exhibit constant, increasing, or decreasing returns to scale?…arrow_forwardA firm faces the following production function, Y = AKa L¹-a (1) Here Y is output, K is capital, L is fixed labour, and A is a measure of technology. The firm uses an optimal amount of capital determined by the condition, (2) MPK = r + 8 Where MPK is the marginal productivity of capital, r is the real interest rate, and Ổ is the depreciation rate. Suppose that a = 0.5, L = 25, and A = 20. Further, the real interest rate, r, is 2% and capital depreciates at a rate (8) of 18% per year. What is the optimal amount of capital this firm should install? [2 marks] Now suppose that A increases to 25, while a, L and & remain unchanged. Further, the optimal capital stock remains at the amount you found in part (c). What does this mean must have happened to the real interest rate? Find the new real interest rate and draw a clear diagram showing MPK and user cost of capital lines before and after the changes to A and r. [4 marks]arrow_forwardSuppose a Cobb-Douglas Production function is given by the following: P(L, K) = 70L0.9K01 where L is units of labor, K 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 $1,000 and each unit of capital costs $7,000. Further suppose a total of $2,800,000 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, L = Units of capital, K = 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 =arrow_forward
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