Answer to Question #90233 in Microeconomics for Faith C Eke

Question

1. Given that the demand curve of a monopolist are x=50-0.5p . The cost function “c”=50+40x . The goal of the firm is profit maximization where profit = Tr -Use equal marginal principle to get the quantity demanded , price and show that the second order condition for profit maximization is fulfilled (15marks)get the profit for the monopoly as well

2. x=50-0.5p.
X1=32-0.4p1
X2=18-0.1p2
Where monopolist practice price discrimination x1+x2=x
C=50+40x=50+40(x1+x2)
aFind monopolists profit
Find mr in each market
Find price in each market
Find Tc for the industry

Answer 1

1. x = 50 - 0.5p, so p = 100 - 2x.

Profit is maximized when MR = MC.

MR = TR' = 100 - 4x,

MC = TC' = 40.

100 - 4x = 40,

x = 15 units.

p = 100 - 2×15 = 70.

2. x=50-0.5p, so p = 100 - 2x.

X1=32-0.4p1, so p1 = 80 - 2.5x1, MR1 = 80 - 5x1.

X2=18-0.1p2, so p2 = 180 - 10x2, MR2 = 180 - 20x2,

If C=50+40x=50+40(x1+x2), then MC1 = MC2 = 40.

MR1 = MC1 and MR2 = MC2, so:

80 - 5x1 = 40,

x1 = 8 units,

p1 = 80 - 2.5×8 = 60.

180 - 20x2 = 40,

x2 = 7 units,

p2 = 180 - 10×7 = 110.

C=50+40x=50+40(x1+x2) = 50 + 40×(8 + 7) = 650.

Profit = 60×8 + 110×7 - 650 = 600.