Question

The second picture is the "previous question" that the question is referring too.

Manufacturers.inc has the following production function that represents the available tech- nology to mix capital (K) and labor (L) (their only two inputs): 9(L, K) 3D L'3К?З = in the short run, the firm has a fixed level of capital K = 8 1) Fill the following table. MP. АPL 0 1 3 4 7 9 10 2) Graph total production, M P, and AP according to the values in the table form the previous question 3) Graph the isoquants in the long run from the levels of production q 1,2,3 Answer the following questions using the same production function from problem 1 and the following information: 2/3 1/3 -))". MPL , MPK , w = 2,r = 3 K 1 Due date ECON 302 Homework 5: Producer Theory I May 23, 2019 May 28, 2019 1) Fill the following table thinking of the short run costs of Manufacturers.inc: AC AFC AVC VC МС 1 6 7 8 10 2) Graph accordingly your findings from the previous question. Use one graph for C, F, andVC and another one for AC, AFC, AVC, and MC 3 Draw the isocosts of in the long run having costs of C = 20, 30, 40 4) Find and graph the long run cost function of Manufacturers.inc

Answer 1

At equilibrium, Marginal Rate of Technical Substitution is equal to the ratio of the factor prices. Hence,

К 2 4L K K= 3. 2L 3

Plugging the value of K in the production function,

4L 3 9- 2р- ир3 - L-qG23, к -q 1/3 1/3 2/3 2/3

The cost function of the firm is given by:

3 1/3 Cost 2q2/3 +3q) 4

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.

Cost 60 50 40 30 20 10 0 1 2 4. 5 6 7 10 st

MC and AVC/AC 6 5 Vertical (Value) Axis 3 2 1 0 1 2 3 5 6 7 8 10 MC AVC-

Since there is no fixed cost, the graphs for AVC and AC are the same.

3)

6 -4- 2 4 0 CO N-

The lines further to the right represent higher costs.

4) We have already found the cost function in part 1).

8 6- 4 2 CO CO