<p>The purpose of part b is probably to illustrate what happens during hyper inflation: people spend there money immediately while they get anything for them.</p>
<p>Note that there is probably an implicit constraint that <span class="math-container">$c_2$</span> cannot be lower than <span class="math-container">$0$</span>, so the answer would be <span class="math-container">$c_1 =  6, c_0 = 0.$</span></p>

CC BY-SA 4.0
2018-09-11T14:43:14.530Z
thanks for yr input .
However, I was considering if I should discount the future 3 received to the present value and accounting for inflation as well.
This means that since inflation is 100% , also because of 5% interest, the PV of 3 in c2 would be 3(1+1/1.05). therefore c2 = 3 + 3(2/0.5)
skukkzky
CC BY-SA 4.0
2018-09-12T08:19:07.587Z
No, you should discount it using the interest rate only.
Klas Lindbäck
CC BY-SA 4.0
2018-09-11T13:52:11.943Z
2021-07-30T10:23:44.483Z
2021-07-30T10:23:44.483Z
Klas Lindbäck
<p>Adam's consumption period 1 and 2 are denoted by $c_1$ and $c_2$ respectively. His utility function is $U(c_1,c_2)=4c_1^{0.5} + c_2$
Ben earns an income of \$3 in period 1 and \$3 in period 2, regardless of the level of inflation.
a.  Suppose there is no inflation and the interest rate is 5%. How much will Ben consume in each period?
b.  Now suppose that inflation rate rise to 100%. How much will Adam consume in each period now?</p>

<p>For part a, I took $c_2= -1.05c_1 + 6.15$ as the budget line and equated it to 
MRS of his utility function. I managed to obtain $c_1 = 3.63$ and $c_2= 2.341$.</p>

<p>However, I am unsure of how to do part b as I obtain a negative answer for $c_2$ after doing the same steps as part a. The only differenece was that I took into account inflation for part b.</p>

CC BY-SA 4.0
2018-09-11T15:14:42.623Z
let m1 =3 , m2 = 3 
c2 = m2 + (1+0.05)/(1+1) * (m1 -c1)
c2= -0.525c1 + 4.575
Equating MRS and slope of budget line,
2c1^(-0.5) = 0.525 ,  c1 = 14.51 , c2 = -3.04
skukkzky
<microeconomics>
intertemporal utility maximisation
skukkzky
# intertemporal utility maximisation

(Asked by: username_0 on 2018-09-11)

Adam's consumption period 1 and 2 are denoted by $c\_1$ and $c\_2$ respectively. His utility function is $U(c\_1,c\_2)=4c\_1^{0.5} + c\_2$
Ben earns an income of \$3 in period 1 and \$3 in period 2, regardless of the level of inflation.
a. Suppose there is no inflation and the interest rate is 5%. How much will Ben consume in each period?
b. Now suppose that inflation rate rise to 100%. How much will Adam consume in each period now?

For part a, I took $c\_2= -1.05c\_1 + 6.15$ as the budget line and equated it to
MRS of his utility function. I managed to obtain $c\_1 = 3.63$ and $c\_2= 2.341$.

However, I am unsure of how to do part b as I obtain a negative answer for $c\_2$ after doing the same steps as part a. The only differenece was that I took into account inflation for part b.

**Tags:** microeconomics
> **Comments:**
> **username_0**: let m1 =3 , m2 = 3  c2 = m2 + (1+0.05)/(1+1) * (m1 -c1) c2= -0.525c1 + 4.575 Equating MRS and slope of budget line, 2c1^(-0.5) = 0.525 ,  c1 = 14.51 , c2 = -3.04  

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## 1 answers

### Answer by username_1 on 2018-09-11. Score: 4

The purpose of part b is probably to illustrate what happens during hyper inflation: people spend there money immediately while they get anything for them.

Note that there is probably an implicit constraint that $c\_2$ cannot be lower than $0$, so the answer would be $c\_1 = 6, c\_0 = 0.$

> **Comments:**
> **username_0**: thanks for yr input . However, I was considering if I should discount the future 3 received to the present value and accounting for inflation as well. This means that since inflation is 100% , also because of 5% interest, the PV of 3 in c2 would be 3(1+1/1.05). therefore c2 = 3 + 3(2/0.5)  
> **username_1**: No, you should discount it using the interest rate only.  

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