The second picture is the "previous question" that the question is referring too.
At equilibrium, Marginal Rate of Technical Substitution is equal to the ratio of the factor prices. Hence,
Plugging the value of K in the production function,
The cost function of the firm is given by:
Using the above function to fill the table given in the question:
q | C | F | VC | AC | AFC | AVC | MC |
0 | 0 | 0 | 0 | - | - | - | - |
1 | 4.882615659 | 0 | 4.882615659 | 4.882615659 | - | 4.882615659 | 4.882615659 |
2 | 9.765231319 | 0 | 9.765231319 | 4.882615659 | - | 2.44130783 | 4.882615659 |
3 | 14.64784698 | 0 | 14.64784698 | 4.882615659 | - | 1.627538553 | 4.882615659 |
4 | 19.53046264 | 0 | 19.53046264 | 4.882615659 | - | 1.220653915 | 4.882615659 |
5 | 24.4130783 | 0 | 24.4130783 | 4.882615659 | - | 0.976523132 | 4.882615659 |
6 | 29.29569396 | 0 | 29.29569396 | 4.882615659 | - | 0.813769277 | 4.882615659 |
7 | 34.17830962 | 0 | 34.17830962 | 4.882615659 | - | 0.697516523 | 4.882615659 |
8 | 39.06092528 | 0 | 39.06092528 | 4.882615659 | - | 0.610326957 | 4.882615659 |
9 | 43.94354094 | 0 | 43.94354094 | 4.882615659 | - | 0.542512851 | 4.882615659 |
10 | 48.82615659 | 0 | 48.82615659 | 4.882615659 | - | 0.488261566 | 4.882615659 |
2) Since there are no fixed costs, F and AFC are
zero for all levels of output.
Since there is no fixed cost, the graphs for AVC and AC are the same.
3)
The lines further to the right represent higher costs.
4) We have already found the cost function in part 1).
The second picture is the "previous question" that the question is referring too. Manufacturers.inc has the foll...
Let K be the level of capital in the short run. The prices of capital and labor are r = 10 and w-5, respectively. For each of the following production functions, (1) derive the short-run cost function (5 pts), (2) derive the long-run cost function (5 pts), and (3) illustrate how you derive the long-run cost function with isoquants and isocosts (5 pts). Hint: for the long-run cost function, first set up the cost minimization problem. (a) (15 pts) f(K,...
1. A production function is given by f(K, L) = L/2+ v K. Given this form, MPL = 1/2 and MPK-2 K (a) Are there constant returns to scale, decreasing returns to scale, or increasing returns to scale? (b) In the short run, capital is fixed at -4 while labor is variable. On the same graph, draw the 2. A production function is f(LK)-(L" + Ka)", where a > 0 and b > 0, For what values of a and...
A firm discovers that when it uses K units of capital and L units of labor, it is able to produce X = L^1/4*K^3/4 units of output. a. Draw the graph of isoquants in labor-capital plane. b. Suppose that the firm produces 24 units of output using 16 units of capital and 81 units of labor. Compute MRTS subscript LK. Compute the MPL. Compute the MPK. c. On the basis of your answer to part (b), is the equation MRTS...
#1 (2 points) What are the relationships that the aggregate production function repre- sents? As a hypothetical example, describe each part of the function as if the variables represent data from the United States. #2 (2 points) In economics, what is the difference between the short run and long run? Is the aggregate production function a short run or long run model? #3 For this question use this aggregate production function: Y = AK1/4 [3/4 Part A) (2 points) Does...
8.13. A firm produces a product with labor and capital. Its production function is described by Q = L + K. The marginal products associated with this production function are MPL = 1 and MPK = 1. Let w= 1 and r = 1 be the prices of labor and capital, respectively. a) Find the equation for the firm's long-run total cost curve as a function of quantity Q when the prices labor and capital are w = 1 and...
QUESTION 5 The marginal product for labor is given (MP) = 3 – 0.02*L; price of the product is $100 and wage = 200. Based on information above, the marginal product of labor at the optimal level of employment is $3 $2 $1.5 $1 2 points QUESTION 6 If the labor elasticity of output is 0.5 and the capital elasticity of output is 0.9, then the production function exhibits constant returns to scale. economies of scale. diseconomies of scale. diminishing...
8. Suppose that the following graph shows a few of the isoquants for a firm's production function for producing park benches. The firm's production function is Q = 20KVL. Suppose that the firm's goal is to produce Q= 160 in the cost minimizing way. The cost of a unit of capital (K) is $32 (r=$32) and the cost of a unit of labor is $32 (w=$32). a. Show the firm's cost minimizing isocost on the graph when the firm is...
Complete the following short-run cost table using the information provided. Total product TFC AFC TVC AVC TC MC 0 0.0 1 3.0 2 5.0 5.0 3 9.0 7. (10 points) Answer the questions below on the basis of the above graph. (a) (3 points-1 point for short run; 1 point for long run; 1 point for how you can tell) How can you tell if these cost curves are for the short run or the long run? (b) (7 points)...
Please solve and show full work for a rating. Thank you. Plastic bags are great 2) The production of plastic bags is given by the production function q K is capital and L is labor. f(LK) s, where Short Run Production a. ) Find the expressions for the Marginal Product of Labor (MP) and Average Product of Labor (APL) in the Short Run, when K is fixed at 400. i) Derive L() in the Short Run, again with K fixed...
2. A firm has the production function y = 4LK. The marginal products are given by MPL = 4K and MPK = 4L. (a) Provide an expression for the long run total cost function. (b) Now suppose that wi = WK = 25. Write out the expression for the long run total cost curve, and plot it on a graph. (C) With wi = wK = 25, derive the long run average cost curve, and plot it on a graph....