U(C1, C2)=C108c20.4 where C1 is the quantity of current consumption goods and c₂ is the quantity of future consumption goods. Consider a consumer whose income is y₁ = 100 in the current period a y2 = 140 in the future period. The consumer pays lump-sum taxes t₁ 20 in the current pe and t₂ = 10 in the future period. The real interest rate is r = 0.1, or 10%, per period. == == (a) Write down the consumer's budget constraint for each period and derive the consume lifetime budget constraint. What is the value of the consumer's lifetime wealth? [Note: Lifetime wealth is the present value of the consumer's lifetime disposable inco

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Chapter1: Making Economics Decisions
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U(C1, C2) = c₁0.8 20.4
where c₁ is the quantity of current consumption goods and c₂ is the quantity of future
consumption goods. Consider a consumer whose income is y₁
=
100 in the current period and
y₂ = 140 in the future period. The consumer pays lump-sum taxes t₁
and t₂
==
=
20 in the current period
10 in the future period. The real interest rate is r = 0.1, or 10%, per period.
(a) Write down the consumer's budget constraint for each period and derive the consumer's
lifetime budget constraint. What is the value of the consumer's lifetime wealth?
[Note: Lifetime wealth is the present value of the consumer's lifetime disposable income]
(b) Draw the lifetime budget line on the (C1, C2) plane with c₁ on the horizontal axis and C₂
on the vertical axis. Include the values of the intercepts and the endowment point in your
graph. What is the slope of the budget line?
(c) What are the two conditions that the consumer's optimal choice of (C1, C2) must satisfy?
Find the consumer's optimal choice of (C1, C2, s). Is the consumer a lender or a borrower?
[Note: By definition, MRSC₁cz
MUC1]
MUC2
(d) Given the consumer's optimal choice, draw a relevant indifference curve on the graph in
(b). Include the values of the optimal quantities of current consumption, future
consumption, and savings in the graph.
Transcribed Image Text:U(C1, C2) = c₁0.8 20.4 where c₁ is the quantity of current consumption goods and c₂ is the quantity of future consumption goods. Consider a consumer whose income is y₁ = 100 in the current period and y₂ = 140 in the future period. The consumer pays lump-sum taxes t₁ and t₂ == = 20 in the current period 10 in the future period. The real interest rate is r = 0.1, or 10%, per period. (a) Write down the consumer's budget constraint for each period and derive the consumer's lifetime budget constraint. What is the value of the consumer's lifetime wealth? [Note: Lifetime wealth is the present value of the consumer's lifetime disposable income] (b) Draw the lifetime budget line on the (C1, C2) plane with c₁ on the horizontal axis and C₂ on the vertical axis. Include the values of the intercepts and the endowment point in your graph. What is the slope of the budget line? (c) What are the two conditions that the consumer's optimal choice of (C1, C2) must satisfy? Find the consumer's optimal choice of (C1, C2, s). Is the consumer a lender or a borrower? [Note: By definition, MRSC₁cz MUC1] MUC2 (d) Given the consumer's optimal choice, draw a relevant indifference curve on the graph in (b). Include the values of the optimal quantities of current consumption, future consumption, and savings in the graph.
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