Rocky has a utility function that can be written as is U(c1,c2)= max {c1,ßc2}. W

Question

Rocky has a utility function that can be written as is U(c1,c2)= max {c1,ßc2}. Where c1 and c2 are his consumption in periods 1 and 2, respectively, and ß is a discount rate with value 0.9, meaning that consumption in period 2 is not valued as much as consumption in period 1. Harvey earns $180 in period 1, and he will earn $77 in period 2. He can borrow and save at an interest rate of 10%. There is no inflation. Which of the following is true?

a) Harvey will save $180

b) Harvey will save $70

c) Harvey will borrow $70

d) Harvey will neither borrow nor lend

e) None of the above.

Also, how would I solve the problem if inflation is involved?

Explanation / Answer

It is stated that consumption in period 2 is not valued as much as consumption in period 1. Because money gets discount at 090% of todays value in period 2.

Now lets consider eac option one by one:

If he saves $180, the value of 180 will be 0.9*180 = 162 and value of 77 will be 0.9*77 = 69.3

and he will get interest at 180 saving = 0.1*180 = 18, making amount = 180+18 = 198 but in period 2 it will be

thus he will have money in period 1 = 0 and in period 2 = 69.3+78.2 = $247.3 which will be less than 180 in period 1 and 77 in period 2 that gives 180 + 69.3 = 249.3. Hence no use.

If he save 70, will get amount = 70 + 7 = 77 that will be equal to 0.9*77 = 69.3 in period 2. Thus total amount in period 2 = 69.3 + 69.3 = 138.6 and in period 1 he will have 180-70 = 110 making total as 138.6+110 = 248.6

But if he does not save he will have 180 in period 1 and 69.3 in 2 making total 249.3 that is more than 248.6 hence again no use.

c)If he borrow 70, he wili have in period 1 = 180+70 = 150 and in period 2 he will have = 77 - 77 as he will make payment of loan with interest = 0 thus making total of 150. hence again no.

thus corrrect option is he will neither borrow nor lend.

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