min (2c1,c2), m1=800000 m2=0, 20% interest rate how much will be consumed in each period?

min (2c1,c2), m1=800000 m2=0, 20% interest rate

how much will be consumed in each period?

Solutions

Expert Solution

We have the utility function as . The first period constraint would be as , for s be savings. The second period constraint would be as , for r be the interest rate. Since we have , the combined constraint would be as or . For the given values, we have or .

Since the utility curve is L-shaped, ie similar to a Leontiff production function, the usual slope equality or Lagrange's process cannot be used to find the utility maximizing combination. Actually, the utility maximizing combination would be where the corner/kink of the L-shaped curve exists, which would be where . For the utility maximizing combination of consumption be or , putting this in the budget constraint, we have or or , and since or , we have or . The savings would be or .

Hence, the consumption in first period would be 300000, and the consumption in the second period would be 600000 (= 500000 saved and 100000 as the 20% interest on the savings).

Rahul Sunny answered 4 months ago

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