Harvey Habit has a utility function U(c 1 , c 2 )  min  c 1 , c 2  , where c 1 and c 2 are his consumption in periods 1 and 2 respectively.Harvey earns $147 in period 1 and he will earn $63 in period 2.Harvey can borrow or lend at an interest rate of 10%.There is no inflation.A) Harvey will save $102.B) Harvey will borrow $40.C) Harvey will neither borrow nor lend.D) Harvey will save $40.E) None of the above.

Question

Harvey Habit has a utility function U(c 1 , c 2 )    min  c 1 , c 2  , where c 1  and c 2  are his consumption in periods 1 and 2 respectively.Harvey earns $147 in period 1 and he will earn $63 in period 2.Harvey can borrow or lend at an interest rate of 10%.There is no inflation.A) Harvey will save $102.B) Harvey will borrow $40.C) Harvey will neither borrow nor lend.D) Harvey will save $40.E) None of the above.

myles howard · Accepted Answer

Final Answer : D, Explanation :  To maximize his utility, Harvey needs to allocate his consumption between the two periods in a way that maximizes his overall satisfaction. We can solve for his optimal consumption using the following equation:MRS = (MU1/MU2) = (1+r)MU1 = U1, MU2 = U2Taking the partial derivative of U with respect to c1 and c2, we can derive the following conditions for Harvey's optimal consumption:MU1/MU2 = (1+r)MU1/P1 = MU2/P2Plugging in the values for U, P1, P2, and r, we get:(c 1 /2) / (c 2 /2) = 1.1(c 1 /2) / 147 = (c 2 /2) / 63Solving for c1 and c2, we get:c 1  = 90c 2  = 210Harvey's total consumption over the two periods will be 300. Given that he earns $147 in period 1 and will earn $63 in period 2, he will have a total income of $210. Therefore, he will save $40 to finance his consumption in period 2, as his optimal consumption for period 1 exceeds his income in that period. Option D is the correct answer.

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