Question

Section 1: Using marginal analysis to determine the profit maximizing price and quantity of resources in a factor market under perfect

Orange Inc. sells cell phones in a perfectly competitive market in the short-run. Capital and labor are two resource factors used to produce the cell phones. Capital is fixed in the short-run but labor can vary. The market for hiring labor is a perfectly competitive market.

Labor is measured in worker weeks. Each worker week costs $700 of wages and Orange Inc. can hire any number of worker weeks. Each cell phone is sold at a price of $300 and can sell any number of phones that are produced. Information is given below on various amounts of labor and output.

Table 1:

Quantity of Labor (in worker weeks)	Output of Phones (per week)
0	0
1	7
2	13
3	18
4	22
5	25
6	27

Step 1

Using the information preceding Table 1 and the table, create a separate table that includes the following for each quantity of labor value: marginal product of labor, total revenue, marginal revenue, marginal revenue product of labor, total variable cost, marginal cost, total resource cost, and marginal resource cost.

The table can be computer-generated or created by hand. Be sure to appropriately label the table so the various calculated values can be identified. Round off to two decimal places for the dollar values.

Step 2

Using the table you created in Step 1, create a graph that illustrates the profit maximizing level of output price and output quantity for the company using marginal analysis.

The graph can be computer-generated or created by hand. Indicate the profit maximizing output quantity and output price in this graph.

Step 3

Using the table you created in Step 2, create a graph that illustrates the profit maximizing level of input price and input quantity for the company using marginal analysis.

The graph can be computer-generated or created by hand. Indicate the profit maximizing input quantity and input price in this graph.

Step 4

In a short paragraph (100 to 200 words), indicate the profit for Orange Inc. (assuming the company maximizes profit) using the information you calculated in the table for Step 1. In addition, explain how the optimal input and optimal output decisions for Orange Inc. are equivalent

Answer 1

a) we have calculated MR = change in TR/change in q = price because MR is the addition to revenue due to an additional unit sold (which is price here). MC = change in TC/change in q because MC is change in Tc with an additional unit of output produced.

P(price)	300
W(wages)	700
Quantity of Labor (in worker weeks)	Output of Phones (per week)	Marginal product	TR = p*q	MR = change in TR/change in q	MRP = MR*MP	TVC = L*wage	MC = change in TC/change in q	MRC = wage = change in Tc/change in labor	MRP/MRC
0	0		0		0	0
1	7	7	2100	300	2100	700	100	700	3
2	13	6	3900	300	1800	1400	116.67	700	2.6
3	18	5	5400	300	1500	2100	140	700	2.1
4	22	4	6600	300	1200	2800	175	700	1.7
5	25	3	7500	300	900	3500	233.33	700	1.3
6	27	2	8100	300	600	4200	350	700	0.9

b)

profit maximising level of output would be where MR = MC which lies at a q level between 25 and 27.

c)

profit maximising level of input will be where MRP of additional labor week ie equal to MRC of additional labor week. which is between and 6 labor weeks.

D) both decisions in part b and c point to employing labor weeks in (5,6) range that will produce output in (25,27) range. this is because profit maximisation from deciding q level is same as cost minimisation decision with respect to L.