3) Derive Manuel's optimal bundle x₁*, X₂* as a function of his income (mm) and p₁ (show your work). 4) Suppose the market has a total of 20 consumers. Ten consumers are identical to Karol, and ten are identical to Manuel. Find the market demand curve for kombucha as a function of mk, mm, and p1. If mk = mM = 100, and p₁=2, what is the total amount of kombucha that the consumers demand?
3) Derive Manuel's optimal bundle x₁*, X₂* as a function of his income (mm) and p₁ (show your work). 4) Suppose the market has a total of 20 consumers. Ten consumers are identical to Karol, and ten are identical to Manuel. Find the market demand curve for kombucha as a function of mk, mm, and p1. If mk = mM = 100, and p₁=2, what is the total amount of kombucha that the consumers demand?
Chapter21: Demand: Consumer Choic
Section: Chapter Questions
Problem 16E
Related questions
Concept explainers
Marginal Rate of Technical Substitution
MRTS reaches a manufacturer when a part of the product is lowered to sustain the manufacturing level when the other part is extended. It is the level of the quantity that is lowered when one extra volume is used, and the output is unchanged.
Preferences and Utility Analysis
Before understanding what is preference and utility analysis, it is very important to understand the terms preference and utility separately.
Question
Transcribed Image Text:Two friends, Karol and Manuel, like to drink
kombucha (x₁) and matcha (x₂). Both X₁ and X2
are expressed in ounces.
The following utility function represents Karol's
preferences:
1
1
2 2
u (x₁, x₂) = x ₁ x ²
The following utility function represents
Manuel's preferences:
u (x₁, x₂) = √√x1 + x2
Karol's income in dollars is denoted by mk, and
Manuel's income is denoted by mm. Both face
the same prices in the market, denoted by p₁
and p2, for kombucha and matcha, respectively.
Both prices are expressed in dollars per ounce.
Assume p2=1 throughout the whole question.
Transcribed Image Text:3) Derive Manuel's optimal bundle x₁*, X2* as
a function of his income (mm) and p₁ (show your
work).
4) Suppose the market has a total of 20
consumers. Ten consumers are identical to
Karol, and ten are identical to Manuel.
Find the market demand curve for kombucha as
a function of mk, mm, and p1.
If mk
mM = 100, and p₁=2, what is the total
amount of kombucha that the consumers
demand?
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