A manufacturer of flash drives has a profit function =52=t5q2 where t is the price charged for a flash drive and 2q2 is the cost of producing a drive whose capacity is q gigabytes. A consumer of type has a utility function =u=qt, where takes on a value of 15 for H-type consumers, or 11 for L-type consumers. There are 10 consumers of each type. A consumer gets zero utility if she does not buy.

Answer the following. If rounding is needed, round to 3 decimal points.

a) (0.25 point) Suppose (,)(q^L,t^L) is the optimal (profit maximising) capacity-price bundle for L-type consumer under complete information. What is the value of t^L?

Answer for part 1

b) (0.25 point) Suppose (,)(q^H,t^H) is the optimal (profit maximising) capacity-price bundle for H-type consumer under complete information. What is the value of t^H?

Answer for part 2

c) (0.5 points) What is the seller's overall profit under complete information?

Answer for part 3

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

d) (0.5 point)

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 type L consumer from buying the (,)(q^H,t^H) bundle? That is, what is (,)uL(q^H,t^H)?

Answer for part 4

e) (1 points) What is the utility for the type H consumer from buying the (,)(q^L,t^L) bundle? That is, what is (,)uH(q^L,t^L)?

Answer for part 5

f) (1 point) What are the seller's profits if he offers the bundles (,)(q^L,t^L) and (,)(q^H,t^H) when information is asymmetric?

Answer for part 6

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) (1 point)For H-type consumer, what is the optimal (profit maximising) level of qH?

Answer for part 7

h) (1 point) Suppose (,)(qL,tL) is the optimal (profit maximising) capacity-price bundle for L-type consumer under asymmetric information. What is the value of tL?

Answer for part 8

i) (0.5 points) 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?