a
To find:Labor, fuel, capital input production elasticities.
a
Answer to Problem 9E
Labor production elasticity = 0.45
Capital production elasticity= 0.30
Fuel production elasticity= 0.20
Explanation of Solution
Given Information:
The production function is given as:
Taking log both the sides:
Introduction:
Labor input production elasticity is a measurement of percentage change in output due to percentage change in labor. It shows productivity of labor.
Fuel input production elasticity is a measurement of percentage change in output due to percentage change in fuel. It shows productivity of fuel.
Capital input production elasticity is a measurement of percentage change in output due to percentage change in capital. It shows productivity of capital.
b)
To ascertain:Percentage change in output due to change in labor input.
b)
Answer to Problem 9E
Percentage change in output due to change in labor input is 0.90.
Explanation of Solution
Given Information:
Increase in labor input = 2%
Percentage change in
It is given that percentage change in labor is 2 percentage. Hence,
Introduction:
Labor input production elasticity is a measurement of percentage change in output due to percentage change in labor. It shows productivity of labor.
c)
To find:Percentage change in output due to change in capital input.
c)
Answer to Problem 9E
Percentage change in output due to change in capital input is -0.90.
Explanation of Solution
Given Information:
Decrease in capital = 3%
Percentage Change in
It is given that percentage change in capital is -3 percentage. Hence,
Introduction:
Capital input production elasticity is a measurement of percentage change in output due to percentage change in capital. It shows productivity of capital.
d)
To know:Types of returns to scale.
d)
Answer to Problem 9E
It is decreasing returns to scale.
Explanation of Solution
Given Information:
This represents decreasing returns to scale.
There are decreasing returns to scale.
Introduction:
Returns to scale is the output growth due to input change. It measures change in output due to change in all factor inputs. It is a long run phenomenon.
e)
To ascertain:Problems due to time series data for estimating parameters of model.
e)
Explanation of Solution
Certain problems due to time series data are:
- Variables are interdependent on each other which leads to incomplete analysis of single variable.
- Time series data are not used for prolonged time duration. Analysis fails after a certain period of time.
- Labor, capital or fuel input may be efficient at certain time period but may become inefficient after certain period after an optimal usage of any of the inputs.
Want to see more full solutions like this?
Chapter 7 Solutions
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
- The output (Q) of a production process is a function of two inputs (L and K) and K is given by the following relationship: Q = 0.50LK− 0.10L2− 0.05K2 The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is interested in maximizing output subject to a cost constraint of $500. Use the lagrangian optimization techniques to find the following: How many units of L and K should be used by the firm? What is the total output of this combination? What is the marginal rate of substitution between L and K?arrow_forwardIntroduction to Calculus in Economics: Calculus is a powerful tool used in economics. One of the initial applications areas is the study of a firm, a topic in microeconomics. An important function is the cost function function C (x), the cost of producing z items (of whatever they are selling). This question deals with just the cost function C (x). Problem Set question: The cost, in dollars, of producing a units of a certain item is given by C (x) = 10x – 10T -9. Find the production level that minimizes the average cost per unit. The number of units that minimizes the average cost isarrow_forwardConsider the production function: Q = 2K + 3L. The MRTSLK is:arrow_forward
- Let C(T) be a function that models the dependence of the cost (C) in thousands of dollars on the amount of ore to extract from a copper mine measured in tons (T): 1) If you computed the average rate of change of cost with respect to tons for production levels between T = 20000 and T = 40000, give the units of your answer (no calculations - describe the units of the rate of change). 2) If you had a function for C(T) and were able to calculate the answer to part 1, explain why you would not expect your answer to be negative (explanation should be in terms of cost, tons of ore to extract, and rates of change).arrow_forwardIntroduction to Calculus in Economics: Calculus is a powerful tool used in economics. One of the initial applications areas is the study of a firm, a topic in microeconomics. An important function is the cost function function C (z), the cost of producing z items (of whatever they are selling). This question deals with just the cost function C (z). Problem Set question: The cost, in dollars, of producing z units of a certain item is given by C (z) = 5z – 8/I – 3. Find the production level that minimizes the average cost per unit. The number of units that minimizes the average cost is Numberarrow_forwardTable: Production Function for Soybeans Quantity of labor (workers) 0 1 2 3 4 5 Quantity of soy beans (bushels) 25 45 60 70 75 034822 The fixed inputs are 10 acres of land and a tractor. They have a combined cost of $150 per day. The cost of labor is $100 per worker per day. Producing 45 bushels of soybeans would result in: TC= ATC= AVC= AFV =arrow_forward
- 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?arrow_forwardConsidering the Production Function Y = 95 - 2X,2 + 3X, + 5X,X2 - 6X22 + 18X2 Find the values of X1:X, and TPParrow_forward100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.arrow_forward
- Answer with solutionarrow_forwardAnswer all questions otherwise skip.arrow_forwardPepper farming is carried out in a greenhouse. Proceeds from the sale of pepper, R,dollars per square meter is determined by the following function. R = 5T (1-e^-x) where T is the temperature set in the greenhouse (Celsius, C^0)and the amount of fertilizer per square meter (kilogram, kg) the costs are as follows: fertilizer cost per square meter is 20?, heating cost is 0.10^2.According to this information a) type the profit function of the manufacturer,?(?, ?).B) determine the end points of the profit function.c) show which endpoints you specify or which ones give the highest amount of fertilizer with the temperature value that makes the profit.arrow_forward
Managerial Economics: Applications, Strategies an...EconomicsISBN:9781305506381Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. HarrisPublisher:Cengage Learning
Economics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage Learning
