Question

In: Economics

Suppose consider the imperfect substitute indifference curve given by TU (L,M) = 5L1/5 M4/5; MUL =...

Suppose consider the imperfect substitute indifference curve given by

TU (L,M) = 5L^1/5 M^4/5;

MU_L = L^-4/5 M^4/5and wage = $10.

MU_M = 4 L^1/5 M^-1/5 .

M = money income

L = hours of leisure

What the marginal Rate of substitution of the indifference?
What is the optimal allocation of hours of leisure and money income?

Expert Solution

We have the utility as . The budget constraint would be , where H is the hours worked, and since , we have , and the constraint would be or or .

(a) The MRS would be as , since we would have and or or or . In this case, it would be or .

(b) The optimal allocation would be where the MRS is equal to the slope of the budget line, which is as or .

Equating both, we have or or . Putting this in the budget constraint, we have or or , and since , we have or or .

Hence, the optimal allocation of hours of leisure is 4.8 hrs, while money income is $192.

Rahul Sunny answered 1 year ago

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