12. Sounds familiar?.. maybe, maybe not? (15 points) Show your calculations. Tum

Question

12. Sounds familiar?.. maybe, maybe not? (15 points) Show your calculations. Tummy Fullfigured has an intertemporal utility function which can be specified as U(ci,c2)- min(ei,ßc2. Where ci and c2 are his consumption in periods 1 and 2, respectively, and is a discount rate with value 0.95, meaning that consumption in period 2 is not valued as much as consumption in period 1. Tummy earns $180 in period 1, and he will earn $77 in period 2, He can borrow at an interest rate of 10% and lend (save) at the same interest rate of 10%. There is no inflation. Which of the following is true? a) Tummy will save S50 b) Tummy will borrow $50 o Tummy will sitherborrow no end e) None of the above, Tummy will save: f) None of the above, Tummy will borrow: 13. Rocky Boloní

Explanation / Answer

Consider the given problem, here the utility function is given by, “U=min(C1, bC2), where b=0.95.

So, at the optimum given the utility function, C1 = b*C2. Tummy earn Y1=$180 in period-1and Y2=$77 in period-2 and the rate of interest is r=10%. So, the budget line be, “C1 + C2/(1+r) = Y1 + Y2/(1+r)”.

So, at the optimum C1=b*C2, by putting this in to the budget line we have,

=> C1 + C2/(1+r) = Y1 + Y2/(1+r), => b*C2 + C2/(1+r) = Y1 + Y2/(1+r),

=> [b + 1/(1+r)]*C2 = Y1 + Y2/(1+r), => (0.95 + 1/1.1)*C2 = 180 + 77/(1.1),

=> (0.95 + 1/1.1)*C2 = 180 + 70 = 250, => 1.86*C2 = 250, => C2 = 250/1.86 = 134.4 = 134.

=> C1 = b*C2 = 0.95*134 = 125.3 < 180.

=> tummy is a saver and will save of amount “180-125.5=54.5=55.

=> “C” be the correct option.

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