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