Concept explainers
a.
To draw: Isoquants at output of 1000 boxes of puffed rice per hour.
a.
Explanation of Solution
The given production function is given by
Where K is the number of puffing guns used and L is the number of workers hired each hour.
When q is 1000, the value of
The isoquant shall be made by joining the points which provide answer to such function, this shall, random numbers can be taken for K, to calculate the value of L.
Value of K | Calculation | Value of L |
10 | 10 | |
25 | 4 | |
4 | 25 |
Introduction: Isoquants are
b.
To calculate: Value of L when K is 10 and average labor productivity.
b.
Explanation of Solution
The given production function is given by
Where K is the number of puffing guns used and L is the number of workers hired each hour.
When q is 1000, the value of
Therefore, when the value of K is 10, the value of L must be
In other words, when 10 puffing guns are employed, 10 workers must work each hour to produce 1000 boxes of puffed rice.
Introduction: For any given value of labor (L) or capital (K), one can be calculated from the other by inputting the available value in the production function.
Average productivity refers to the arithmetic mean of total production with total labor input employed.
c.
To state: Impact of technical progress on sub-part (a) and (b).
c.
Explanation of Solution
The new production function is given by
Where K is the number of puffing guns used and L is the number of workers hired each hour.
When q is 1000, the value of
The isoquant shall be made by joining the points which provide answer to such function, this shall, random numbers can be taken for K, to calculate the value of L.
Value of K | Calculation | Value of L |
2 | 12.5 | |
5 | 5 | |
10 | 2.5 | |
12.5 | 2 |
As stated in sub part (b), value of one variable may be calculated by inputting the other in production function, therefore, when the value of K is 10, L shall be
Introduction: Isoquants are curves that represent same level of output at various combination of inputs and are used in determining efficient input mix for lower operational costs.
Average productivity refers to the arithmetic mean of total production with total labor input employed.
d.
To state: Impact of technical progress on sub-part (a) and (b).
d.
Explanation of Solution
The new production function is given by
Where K is the number of puffing guns used and L is the number of workers hired each hour.
The value of
Separate isoquants will be observed every year since the input required to produce the desired output of 1000 boxes would undergo shift.
When q is 1000, the value of
In order to plot the isoquants, arbitrary value of one variable can be taken to find the other variable.
Year | Required K x L |
1 |
|
2 |
|
3 |
|
The isoquant shall be made by joining the points which provide answer to such function, this shall, random numbers can be taken for K, to calculate the value of L.
Using ‘1’, ‘2’ and ‘3’ to denote the years values for K and L at various levels shall be as follow:
K1 | L 1 | K2 | L 2 | K3 | L 3 |
5.00 | 18.14 | 5.00 | 16.45 | 5.00 | 14.92 |
10.00 | 9.07 | 10.00 | 8.23 | 10.00 | 7.46 |
15.00 | 6.05 | 15.00 | 5.48 | 15.00 | 4.97 |
Isoquants can be drawn based on the calculated data as:
As stated in sub part (b), value of one variable may be calculated by inputting the other in production function, therefore, when the value of K is 10, L shall be
Since technical progress is constant year on year, average productivity per hour will increase year on year as well.
Introduction: Isoquants are curves that represent same level of output at various combination of inputs and are used in determining efficient input mix for lower operational costs.
Average productivity refers to the arithmetic mean of total production with total labor input employed.
Technical progress refers to increase the productivity factor, thereby increasing the production with same available inputs.
Want to see more full solutions like this?
Chapter 6 Solutions
EBK INTERMEDIATE MICROECONOMICS AND ITS
- What is the difference between a fixed input and a variable input?arrow_forwardThe production function at Giovanni pizza is Q = 1000 x min (L, 3K) Where Q = pizzas per hour, L is the number of workers, and K is the number of pizzas ovens. - If L = 5 and K = 1, what is the value of Q? Please show your calculations. - What is the additional output when one additional unit of labor is hired?arrow_forward1. A firm can manufacture a product according to the production function Q = F(K,L) = K³/4L¹/4 a. Calculate the average product of labour, when the level of capital is fixed at 16 units and the firm uses 16 units of labour. How does the average product of labour change when the firm uses 81 units of labour? b. Find an expression for the marginal product of labour when the amount of capital is fixed at 16 units. Then, illustrate that the marginal product of labour depends on the amount of labour hired by calculating the marginal product of labour for 16 and 81 units of labour. c. Suppose capital is fixed at 16 units. If the firm can sell its output at a price of £100 per unit and can hire labour at £25 per unit, how many units of labour should the firm hire to maximise profits?arrow_forward
- A firm has the production function f(X, Y) = x²/2 y1/2, where X is the amount of factor x used and Y is the amount of factor y used. On a diagram we put X on the horizontal axis and Y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of -3. The straight line we drew Select one: O a. is vertical. b. is horizontal. c. is a ray through the origin with slope 3. d. is a ray through the origin with slope 4. O e. has a negative slope.arrow_forwardProvide a graph and an explanation to show that the production function Q = L.5K.5 has diminishing marginal product of labor but has constant returns to scale.arrow_forwardWhat is the difference between a fixed input and a variable input?arrow_forward
- With a Cobb-Douglas production function of Y = K²$Ls, What are the marginal product of capital and the marginal product of labor?arrow_forwardSuppose the production function is given by Q = 5K+2L. What is the marginal product of capital when 5 units of capital and 10 units of labor are employed?arrow_forwardA firm can manufacture a product according to the production function:Q=F(K,L)=K^(3/4) L^(1/4).a.Calculate the average product of labour, AP_L, when the level of capital is fixed at 81 units and the firm uses 16 units of labour. How does the average product of labour change when the firm uses 256 units of labour? b.Find an expression for the marginal product of labour, MP_L, when the amount of capital is fixed at 81 units. Then, calculate the marginal product of labour for 16 and 81 units of labour. c.Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit and can hire labour at $50 per unit, how many units of labour should the firm hire in order to maximize profits?arrow_forward
- A firm's production function is given by Q = 20L0.8 K0.2. At that moment, the firm sets = 1,000 and K = 1,000. Which of the following combinations of L and Klies on the same isoquant? L = 1,063.9; K = 698.7 L= 1,063.9; K = 698.7 L=698.7; K = 1,063.9 L = 1,302.3; K = 936.1 L 936.1; K 1,302.3arrow_forwardA firm can manufacture a product according to the production function: Q = F(K, L) = K3/4L1/4.a. Calculate the average product of labor, APL, when the level of capital is fixed at 81 units and the firm uses 16 units of labor. (Enter your responses rounded to three decimal places)(Part of A): What is the average product of labor when the firm uses 256 units of labor?Answer:b. Find an expression for the marginal product of labor, MPL, when the amount of capital is fixed at 81 units. (The second response is the exponent on L in the expression. Enter your responses rounded to two decimal places).MPL = × L ^ Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor. (Enter your responses rounded to three decimal places).MPL when L = 16: MPL when L = 81: c. Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit of output and can hire labor at…arrow_forwardInstructions: Move the slider at the bottom of the diagram to change the quantity of labor hired for both graphs and the table. Move the production slider to 6 units of labor. Suppose you had the information for the L=2 row and the L=6 row, but the row(s) in between them were missing and you didn't have any information in the Marginal Product column. If you wanted to estimate the marginal product, you might assume the marginal products of each of the 4 additional workers are equal. a. Estimate the marginal product of each additional worker if L were to increase from 2 to 6. b. Calculate the slope of the total production function between L=2 and L=6.arrow_forward
- Managerial Economics: Applications, Strategies an...EconomicsISBN:9781305506381Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. HarrisPublisher:Cengage Learning
- Microeconomics: Principles & PolicyEconomicsISBN:9781337794992Author:William J. Baumol, Alan S. Blinder, John L. SolowPublisher:Cengage LearningExploring EconomicsEconomicsISBN:9781544336329Author:Robert L. SextonPublisher:SAGE Publications, Inc