Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

300 INPUT PRICING AND EMPLOYMENT [CHAP. 13
(a)
This firm will maximize its total profits or minimize its total losses when it produces 200X at a SMC of $2 and
an AVC of $4, and sells commodity X at the price of $6. At that point,
(see Fig. 13-16).
MP a
P a
¼ MP b
P b
(b) If the firm produced 150X at an AVC of $5,
MP a
P a
¼ MP c
P c
¼ 1
MC x
¼ 1
MR x
¼ 0:50
¼ MP b
P b
¼ MP c
P c
¼ 1 1 . 1 4
and the firm would not be maximizing its total profits. As the firm increases its output, its SMC increases and
its MR decreases. This firm should continue to expand its output until the output of 200X is reached where
SMC x ¼ MR x ¼ $2 and the AVC x ¼ $4. If the firm produced 250X at minimum cost,
MP a
P a
¼ MP b
P b
¼ MP c
P c
¼ 1
3:5 , 1 0
or better,
P a
MP a
¼ P b
MP b
¼ P c
MP c
¼ 3:5 . 0
and the firm would not be maximizing its total profits. As the firm decreases its output, its SMC decreases and
its MR increases. This firm should continue to reduce its output as long as its SMC . MR and until (at the
output of 200X) they are equal (and the AVC x ¼ $4).
13.15 Table 13.6 refers to the monopolistic seller of commodity X, when input A is the firm’s only variable
input. Find the firm’s MP a ,TR x ,MR x , VMP a , and MRP a schedules.
Table 13.6
q a 2 3 4 5 6 7
Q x 10 20 28 34 38 40
P x ($) 2.00 1.08 1.60 1.40 1.20 1.00
P a ($) 8.80 8.80 8.80 8.80 8.80 8.80
In Table 13.7, MP a [column (3)] ¼ DQ x /Dq a ;TR x [column (5)] ¼ (Q x )(P x ); MR x [column (6)] ¼ DTR x /DQ x ;
VMP a [column (7)] ¼ (MP a )(P x ); MRP a ¼ DTR x /Dq a ¼ (MP a )(MR x ). Note that if commodity X had been sold in
a perfectly competitive market, MR x ¼ P x and the VMP a ¼ MRP a . Since the monopolist must lower P x in order to
sell more of commodity X, MR x , P x and declines. Thus, the MRP x values in column (8) are less than the
corresponding values of the VMP a in column (7) and the MRP a schedule falls both because the MP a falls (since
we are in stage II of production) and because the MR x falls (since we have imperfect competition in the market
for commodity X).
(1) (2) (3) (4)
q a Q x MP a P x ($)
Table 13.7
(5)
TR x ($)
(6)
MR x ($)
(7)
VMP a ($)
(8)
MRP a ($)
(9)
P a ($)
2 10 ... 2.00 20.00 ... ... ... 8.80
3 20 10 1.80 36.00 1.60 18.00 16.00 8.80
4 28 8 1.60 44.80 1.10 12.80 8.80 8.80
5 34 6 1.40 47.60 0.47 8.40 2.80 8.80
6 38 4 1.20 45.60 20.50 4.80 22.00 8.80
7 40 2 1.00 40.00 22.80 2.00 25.60 8.80