A manufacturer of flash drives has a profit function =t2q^2wheretis the price charged for a flash drive andq^2 is the cost of producing a drive whose capacity isqgigabytes. A consumer of type has a utility functionu=qt, where takes on a value of 12 forH-type consumers, or 9 forL-type consumers.

There are 10 consumers of each type. A consumer gets zero utility if she does not buy.If a consumer is indifferent between buying two flash drives, assume she will buy the one with more gigabytes. If a consumer is indifferent between buying a flash drive and not buying, assume she will buy.

a) Suppose(q^L,t^L)is the optimal (profit maximising) capacity-price bundle for L-type consumer under complete information. What is the value oft^L?

b) Suppose(q^H,t^H)is the optimal (profit maximising) capacity-price bundle for H-type consumer under complete information. What is the value oft^H?

c) What is the seller's overall profit under complete information?

For part d) - i), assume information is asymmetric.

d) Suppose that the seller continues to offer the capacity-price bundles that maximises his profit under complete information: that is, he offers(q^L,t^L)and(q^H,t^H). What is the utility for the Lconsumer from buying the(q^H,t^H)bundle? That is, what isuL(q^H,t^H)?

e) What is the utility for the Hconsumer from buying the(q^L,t^L)bundle? That is, what isuH(q^L,t^L)?

f) What are the seller's profits if he offers the bundles(q^L,t^L)and(q^H,t^H)when information is asymmetric?

Now suppose the seller decides to offer a menu of capacity-price bundles(qL,tL)and(qH,tH)to incentives the two types of consumers to sort themselves out. Answer part g) to i) in this context.

g)ForH-type consumer, what is the optimal (profit maximising) level of qH?

h) Suppose(q*L,t*L)is the optimal (profit maximising) capacity-price bundle forL-type consumer under asymmetric information. What is the value oft*L?

i) What is the seller's overall profit under asymmetric information if the seller offers a menu of profit maximizing capacity-price bundles(qL,tL)and(qH,tH)to consumers?