U(C1, C2) = c₁0.8 20.4where c₁ is the quantity of current consumption goods and c₂ is the quantity of futureconsumption goods. Consider a consumer whose income is y₁=100 in the current period andy₂ = 140 in the future period. The consumer pays lump-sum taxes t₁and t₂===20 in the current period10 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'slifetime 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 C₂on the vertical axis. Include the values of the intercepts and the endowment point in yourgraph. 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, MRSC₁czMUC1]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, futureconsumption, and savings in the graph.

Utility function : U (c1 , c2) = c10.8 c20.4In period 1 -Income : y1 = 100 t1 = 20 In period 2…

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

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

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.2P

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