Please solve the last 3 parts A consumer's utility function is:U(c,c) = c,C2where c, and c2 denote the planned consumption of composite good in period 1 and period 2,respectively. The consumption is on composite good and is expressed in rupees. Suppose thereis no inflation, so the prices of the composite good in each period are constant at 1 rupee.1The amount of money (income or endowment) the consumer will have in each period is denotedby m, and m2. The consumer can borrow or save (lend) money at some interest rate r.(a) Write the consumer's utility maximization problem. Define the Lagrangian function forthis utility maximization problem. Write the first order necessary conditions.(b) Find the optimal choice of composite good for each period as function of endowments andinterest rate.(c) Assume: m, = 200, m2 = 100, and r = 0.1. Find the optimal choice of composite goodfor each period (note that it is in rupees). Compute the saving in period 1.(d) Suppose interest rate rises to r = 0.2. Find the optimal choice of composite good for eachperiod. Compute the saving in period 1.(e) Draw a graph showing the effect of increase in the interest rate on saving (draw just twopoints: saving at r = 0.1 andr = 0.2).

Intertemporal choice refers to actions made in the short term, such as spending habits, that might…

A consumer's utility function is: U(C₁, C₂) = C₁ C₂ where c₁ and c₂ denote the planned consumption of composite good in period 1 and period 2, respectively. The consumption is on composite good and is expressed in rupees. Suppose there is no inflation, so the prices of the composite good in each period are constant at 1 rupee. 1

A consumer's utility function is: U(C₁, C₂) = C₁ C₂ where c₁ and c₂ denote the planned consumption of composite good in period 1 and period 2, respectively. The consumption is on composite good and is expressed in rupees. Suppose there is no inflation, so the prices of the composite good in each period are constant at 1 rupee. 1

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Chapter1: Making Economics Decisions

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Question

Please solve the last 3 parts

A consumer's utility function is:
U(c,c) = c,C2
where c, and c2 denote the planned consumption of composite good in period 1 and period 2,
respectively. The consumption is on composite good and is expressed in rupees. Suppose there
is no inflation, so the prices of the composite good in each period are constant at 1 rupee.
1
The amount of money (income or endowment) the consumer will have in each period is denoted
by m, and m2. The consumer can borrow or save (lend) money at some interest rate r.
(a) Write the consumer's utility maximization problem. Define the Lagrangian function for
this utility maximization problem. Write the first order necessary conditions.
(b) Find the optimal choice of composite good for each period as function of endowments and
interest rate.
(c) Assume: m, = 200, m2 = 100, and r = 0.1. Find the optimal choice of composite good
for each period (note that it is in rupees). Compute the saving in period 1.
(d) Suppose interest rate rises to r = 0.2. Find the optimal choice of composite good for each
period. Compute the saving in period 1.
(e) Draw a graph showing the effect of increase in the interest rate on saving (draw just two
points: saving at r = 0.1 andr = 0.2).

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