Question

8-11. A typical consumer has a utility function for cable movies given by the following function: U = 72X -0.15X2 where X is the number of cable movies viewed per year and U is measured in dollars. Questions 8 through 11 concern this consumer. 8. If the price of cable movies is set at $12 per movie, the consumer surplus gained by this typical consumer each year through purchasing cable movies will be: A) $1200 B) $2400 C) $3600 D) $4800 E) $6000 F) $6400 G) $7200 H) $78001) $8200J) none of the above 9. Imagine that the cable company is trying to boost sales. It offers this consumer the following alternative to a price of $12 per movie: the consumer would pay a nominal fee of only $3.00 per movie plus a yearly access charge that would permit the consumer to view as many movies as he or she liked, at no additional charge. The maximum yearly access charge that this consumer would be willing to pay as an alternative to the $12 per- movie fee) would be: A) $120 B) $240 C) $360 D) $800 E) $1760 F) $1935 G) $2400 H) $2640 1) $3200 J) none of the above

Need help with 9, 10 and 11.

Answer 1

8) mu=72-0.3x

Demand function: p=72-0.3x{optimal condition,p=mu}

At p=12. ,X=200

CS=1/2*200*(72-12)=6000(option e is right)

9)it is an example of two part tariff of monopoly.

The maximum yearly charge will be equal to consumer surplus.

At p=3,. X=230

CS=1/2*230*(72-3)=7935(option j is right)

10) Initially at p=12 ,x=200, U=72*200-0.15*200*200=8400

At p=24 ,x=48/0.3=160. U=72*160-0.15*160*160=7680

Utility loss=8400-7680=720( option j is right)

11.) perfectly elastic,only in this situation a tax burden will be fully levied on consumer who have downward sloping demand( our typical CONSUMER have also downward sloping demand).

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