6. Consider a consumer with the utility function u(x1,x2) = In(x) x2 and the budget constraint...

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6. Consider a consumer with the utility function u(x1,x2) = In(x) x2 and the budget constraint px + p2x2 = m. Derive the cons

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Answer 1

Answer #1

u(x₁,x₂) = lnx₁ + x₂

$\partial$ u/ $\partial$ x₁ = MU1 = 1/x₁

$\partial$ u/ $\partial$ x₂ = MU2 = 1

MRS_1,2 = MU1/MU2

= 1/x₁

At optimal choice

MRS = p₁/p₂

1/x₁ = p₁/p₂

x₁ = p₂/p₁

budget constraint

p₁x₁ + p₂x₂ = m

substitute x₁ = p₂/p₁ in budget constraint

p₁( p₂/p₁) + p₂x₂ = m

p₂ + p₂x₂ = m

p₂x₂ = m - p₂

x₂ = m/p₂ - 1

Thus, demand function of x1 and x2

x₁ = p₂/p₁

x₂ = m/p₂ - 1

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Answer 2

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6. Consider a consumer with the utility function u(x1,x2) = In(x) x2 and the budget constraint...

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