Question

Question 4. The Australian Boomerang Company (ABC) sells boomerangs to a market in which there are two types of consumers. One quarter of the consumers place high value on boomerangs, with demand given by qh = 16 - p, where p is the price of boomerangs. The remaining three quarters of consumers place low value on boomerangs, with demand given by ql = 12 – p. ABC has a constant marginal cost of $2 per unit. Suppose first that ABC is able to identify perfectly which consumers are high value and which are low. (a) What is ABC's optimal (i.e., profit maximizing) two-part tariff for the high value con- sumers? (b) What is ABC's optimal two-part tariff for the low value consumers? Suppose now that ABC cannot segment the market (i.e., ABC cannot distinguish between high and low value consumers). (c) What is ABC's optimal two-part tariff? (Hint: A similar problem is analyzed in the Vohra notes, Example 19.]

Answer 1

ANSWER:

Given that:

The Australian boomerang company (ABC) sells boomerangs to a market in which there are two type of consumers. One quarter of the consumers place high value on boomerangs

$q_{H}=16-P$ , $q_{L}=12-P,$ $MC=2$

a) for H type . P = MC=2 , fixed fce = f = CS_H.

  

CSH = 1/2/16 – 21 x 14 = 98

$(p,f)^{H}=(2,98)$

b)

for L type p = MC = 2 , f = CS _L

q_L = 12-2 =10 = 1/2*10*(12-2)=50

c)

can't distinguish charge single fixed fee :

So if f = CS_H = 98 , only high type will participate is market

as only 1/4 th of total customers is high type so,

Let if 4 total customers then total revenue from f = CS_H ( High type ) = 98

If CS_L = f =50 , then both type will participate

so total $\pi$ to mono polist = 4*50 =200 thus higher $\pi$ from f =50

so charge p = MC =2 , fixed fee = 50 .