(a) (b) What is the slope of Douglas' indifference curve at the point (x₁, x2)? If Douglas' budget line is tangent to his indifference curve at (x₁, x2) what is the ratio equal to? (c) P2x2 When he is consuming the best bundle he can afford, what fraction of his income does Douglas spend on ₁? 3x1 P2 Solution: a) His MRS is – 32. b) At the optimal bundle we have, -MRS = P1. Therefore, we have 11 = 2/3. c) Solving for Douglas' demand for each good 3m 1. Therefore, P2I2 2m 1 and ₂: = = 2+3 pi 2+3 p2 in terms of income and prices, we have t he spends 2/5th's of his income on good 1 and 3/5th's on good 2.

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
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Chapter1: Making Economics Decisions
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12.
Douglas Cornfield's preferences are represented by the utility function
u(x₁, x₂) = x²x³ . The prices of x₁ and x₂ are p₁ and P2.
What is the slope of Douglas' indifference curve at the point (x1, x₂)?
If Douglas' budget line is tangent to his indifference curve at (x₁, x2) what is
the ratio 1 equal to?
P2x2
When he is consuming the best bundle he can afford, what fraction of his
income does Douglas spend on x1₁?
P2
3x1
Solution: a) His MRS is – 222. b) At the optimal bundle we have, – MRS = P₁₁
Therefore, we have P₁1
= 2/3. c) Solving for Douglas' demand for each good
2m 1 and ₂ =
3m1 Therefore,
in terms of income and prices, we have x
2+3 pl
he spends 2/5th's of his income on good 1 and 3/5th's on good 2.
P2x2
=
2+3 p2
=
Transcribed Image Text:12. Douglas Cornfield's preferences are represented by the utility function u(x₁, x₂) = x²x³ . The prices of x₁ and x₂ are p₁ and P2. What is the slope of Douglas' indifference curve at the point (x1, x₂)? If Douglas' budget line is tangent to his indifference curve at (x₁, x2) what is the ratio 1 equal to? P2x2 When he is consuming the best bundle he can afford, what fraction of his income does Douglas spend on x1₁? P2 3x1 Solution: a) His MRS is – 222. b) At the optimal bundle we have, – MRS = P₁₁ Therefore, we have P₁1 = 2/3. c) Solving for Douglas' demand for each good 2m 1 and ₂ = 3m1 Therefore, in terms of income and prices, we have x 2+3 pl he spends 2/5th's of his income on good 1 and 3/5th's on good 2. P2x2 = 2+3 p2 =
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