Question

Use the following to answer questions 1-3:

All 20 consumers are alike and each has a demand curve for a monopolist’s product of p= 120 – 2q.  The cost of production C(Q) = 10Q. Let the monopolist charge a price of $r per unit purchased and a subscription fee of $F that must be paid by each purchaser. . Find the r and F that maximize profits?

1)         What is r?

Select one:

A.
  r<0

B.
0≤r<4

C.
  4≤r<8

D.
8≤r<12

E. None of the above

What is F?

Select one:

a.  F<100

b.  100≤F<200

c. 200≤F<300

d.  300≤F

e. None of the above

What is the maximum profit the monopolist can earn in this market? (pi)

Select one:

a.  pi<1,000

b. 1000≤pi<10,000

c. 10,000≤pi<100,000

d.   100,000≤pi

e. None of the above

Answer 1

There is amonopolist in the market who practices second degree price discrimination (two-part tariff). There are 20 consumers with identical demand curve

$demand\ curve\ of\ each\ consumer\\ p=120-2q\\ Cost\ of\ production,TC=10q\\ marginal\ cost,MC=\frac{dTC}{dq}=10\\$

since monopolist uses two part tariff and all the consumers have single type of demand curve.So, the subscription fee charged would be equal to each customer's consumer surplus under perfect competition outcome that is price equals marginal cost.Price charged per unit would be equal to the marginal cost

Part (1)

$\therefore\ price\ charged\ per\ unit\ of\ \$r\ is\ equal\ to\ marginal\ cost\\ r=\$10\\$

correct answer is (d) 8<r < 12

$price\ charged\ per\ unit\ would\ be\ equal\ to\ marginal\ cost\\ p=MC\\ 120-2q=10\\ q=\frac{120-10}{2}=55$

Therefore number units consumed by each consumer would be 55 units

subscription fee, F = area(ABE) F= = * AB * BE= = *(120 - 10) * 55 110 * 55 F= - 2 10 * 55 -= $3,025

Part (2)

correct answer is (e) none of above

$profits,\pi=total\ revenue-total\ cost\\ \pi=(N*F+N*r*q)-(N*MC*q)\\ N=20,F=\$3,025,MC=\$10,q=55,r=\$10\\ \pi=(20*3025-20*10*55)-(20*10*55)\\ \pi=60,500-11,000-11,000=\$60,500$

Part (3)

$correct\ answer\ is\ (c) 10,000 \leq profits,\pi<100,000$