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.

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Chapter1: Making Economics Decisions
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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.
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
Step 1

Given 

Dan's utility function: D(x1,x2)=8.2x1+1.6x22             ......(1)

Lan's utility function: L(x1,x2)=x11.6x28.2                        ...... (2)

Formula for the marginal rate of substitution of good 1 with respect to good 2 is as 

MRS=MU1MU2

Here MUi  denotes marginal utility of ith good.

 

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