Dan's utility function is given by (8.2 x₁ + 1.6x₂)² D(x1, x2) = Lan's utility function is given by L(x₁, x2) = x₁1.6 X₂8.2 where x; denotes the quantity consumed of good i, i =1, 2. Find and compare Dan's marginal rate of substitution (of good 1 in terms of good 2), MRSD, with Lan's marginal rate of substitution, MRSL, at the bundle where x₁ = 4.9 and x2 = 4.2. Then enter below the value of the ratio MRSD/MRSL. Remember every value must be entered below in decimal form.
Dan's utility function is given by (8.2 x₁ + 1.6x₂)² D(x1, x2) = Lan's utility function is given by L(x₁, x2) = x₁1.6 X₂8.2 where x; denotes the quantity consumed of good i, i =1, 2. Find and compare Dan's marginal rate of substitution (of good 1 in terms of good 2), MRSD, with Lan's marginal rate of substitution, MRSL, at the bundle where x₁ = 4.9 and x2 = 4.2. Then enter below the value of the ratio MRSD/MRSL. Remember every value must be entered below in decimal form.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
![Dan's utility function is given by
D(x1, x₂) = (8.2 x₁ + 1.6 x₂)²
Lan's utility function is given by
1.6
8.2
L(X1, x2) = X₁ X2
where x; denotes the quantity consumed of good i, i =1, 2. Find and compare Dan's marginal rate of substitution (of
good 1 in terms of good 2), MRS, with Lan's marginal rate of substitution, MRS, at the bundle where x₁ = 4.9 and x2 =
4.2. Then enter below the value of the ratio MRSD / MRSL.
Remember every value must be entered below in decimal form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04536e59-763c-440c-af8f-4a3fc9711a35%2F8253fa9d-3d75-4f04-b90b-1980980074ff%2Ff9esnr9_processed.png&w=3840&q=75)
Transcribed Image Text:Dan's utility function is given by
D(x1, x₂) = (8.2 x₁ + 1.6 x₂)²
Lan's utility function is given by
1.6
8.2
L(X1, x2) = X₁ X2
where x; denotes the quantity consumed of good i, i =1, 2. Find and compare Dan's marginal rate of substitution (of
good 1 in terms of good 2), MRS, with Lan's marginal rate of substitution, MRS, at the bundle where x₁ = 4.9 and x2 =
4.2. Then enter below the value of the ratio MRSD / MRSL.
Remember every value must be entered below in decimal form.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Given
Dan's utility function: ......(1)
Lan's utility function: ...... (2)
Formula for the marginal rate of substitution of good 1 with respect to good 2 is as
Here denotes marginal utility of ith good.
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Solved in 4 steps
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