A manufacturer of flash drives has a profit function=t-9g2 where t is the price charged for a flash drive and 9g² is the cost of producing a drive whose capacity is a gigabytes. A consumer of type has a utility function=8q-t. where takes on a value of 15 for H-type consumers, or 10 for L-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 capacity. If a consumer is indifferent between buying a flash drive and not buying, assume she will buy. Answer the following. If rounding is needed, round to 3 decimal points. a) Suppose (1,1) is the optimal (profit maximising) capacity-price bundle for L-type consumer under complete information. What is the value of ? 5.55€ b) Suppose (, ) is the optimal (profit maximising) capacity-price bundle for H-type consumer under complete information. What is the value of ? 12.5 c) What is the seller's overall profit under complete information? 9.028 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 (₁, ₂) and (,). What is the utility for the type consumer from buying the (,) bundle? That is, what is (,)? 0 e) What is the utility for the type o consumer from buying the (,) bundle? That is what is uw (LL)? 0 1) What are the seller's profits if he offers the bundles (,) and (,) when information is asymmetric? Now suppose the seller decides to offer a menu of capacity-price bundles (qz, tz) and (g, t) to incentives the two types of consumers to sort themselves out. Answer part g) to i) in this context. g) For H-type consumer, what is the optimal (profit maximising) level of qu? h) Suppose (q,t) is the optimal (profit maximising) capacity-price bundle for L-type consumer under asymmetric information. What is the value of t? i) What is the seller's overall profit under asymmetric information if the seller offers a menu of profit maximizing capacity-price bundles (q, tz) and (q, t) to consumers?
A manufacturer of flash drives has a profit function=t-9g2 where t is the price charged for a flash drive and 9g² is the cost of producing a drive whose capacity is a gigabytes. A consumer of type has a utility function=8q-t. where takes on a value of 15 for H-type consumers, or 10 for L-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 capacity. If a consumer is indifferent between buying a flash drive and not buying, assume she will buy. Answer the following. If rounding is needed, round to 3 decimal points. a) Suppose (1,1) is the optimal (profit maximising) capacity-price bundle for L-type consumer under complete information. What is the value of ? 5.55€ b) Suppose (, ) is the optimal (profit maximising) capacity-price bundle for H-type consumer under complete information. What is the value of ? 12.5 c) What is the seller's overall profit under complete information? 9.028 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 (₁, ₂) and (,). What is the utility for the type consumer from buying the (,) bundle? That is, what is (,)? 0 e) What is the utility for the type o consumer from buying the (,) bundle? That is what is uw (LL)? 0 1) What are the seller's profits if he offers the bundles (,) and (,) when information is asymmetric? Now suppose the seller decides to offer a menu of capacity-price bundles (qz, tz) and (g, t) to incentives the two types of consumers to sort themselves out. Answer part g) to i) in this context. g) For H-type consumer, what is the optimal (profit maximising) level of qu? h) Suppose (q,t) is the optimal (profit maximising) capacity-price bundle for L-type consumer under asymmetric information. What is the value of t? i) What is the seller's overall profit under asymmetric information if the seller offers a menu of profit maximizing capacity-price bundles (q, tz) and (q, t) to consumers?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:A manufacturer of flash drives has a profit function = t - 9q² where t is the price charged for a flash drive and 9q² is the cost of producing a drive whose capacity is a gigabytes. A consumer of type has a utility function u = 0q-t, where takes on a value of 15 for H-type consumers, or 10 for L-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 capacity. If a consumer is indifferent between buying a flash drive and not buying, assume she will buy.
Answer the following. If rounding is needed, round to 3 decimal points.
a) Suppose (91, L) is the optimal (profit maximising) capacity-price bundle for L-type consumer under complete information. What is the value of ↑ L?
5.556
b) Suppose (#,#) is the optimal (profit maximising) capacity-price bundle for H-type consumer under complete information. What is the value of t#?
12.5
c) What is the seller's overall profit under complete information?
9.028
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 (LL) and (t). What is the utility for the type , consumer from buying the (,) bundle? That is, what is uâ, tH)?
|0
e) What is the utility for the type consumer from buying the (â£, £1) bundle? That is, what is up (â L, ÎL)?
0
f) What are the seller's profits if he offers the bundles (â£, £₁) and (â, t) when information is asymmetric?
Now suppose the seller decides to offer menu of capacity-price bundles (q, t) and (qu, t) to incentives the two types of consumers to sort themselves out. Answer part g) to i) in this context.
g) For H-type consumer, what is the optimal (profit maximising) level of qu?
h) Suppose (q, tt) is the optimal (profit maximising) capacity-price bundle for L-type consumer under asymmetric information. What is the value of tt?
i) What is the seller's overall profit under asymmetric information if the seller offers a menu of profit maximizing capacity-price bundles (q₁, t₁) and (¶í, t) to consumers?
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