Question

It's important to have a plan in action when determining the consumer's optimal bundle. Given a pefect substitutes utility function, the prices of the goods, and income write out 3 - 6 steps you would use to solve for the optimal bundle. Be specific.

Answer 1

Steps to solve for the optimal bundle under perfect substitutes utility function:

1. Firstly the utility function for perfect substitutes is U(X,Y) = aX + bY

2. Then , represent the budget line: P_xX + P_YY = M

Where P_X : Price of good X

P_Y : Price of good Y

M : Income of the consumer.

Slope of the budget line = -P_X/ P_Y

3. Now, calculate MRS= MU_X/ MU_Y

MU_x = a and MU_Y =b. MRS = a/b . It represents the slope of the indifference curve which is constant for perfect substitutes.

4. If MRS= MU_X/ MU_Y > P_X/ P_Y or MU_X/ P_X > MU_Y/P_Y. It implies that if an additional unit of utiltiy per dollar spending on good X is greater than the additional unit of utiltiy per dollar spending on good Y, then this means that the consumer spend his entire income on only consumption of one good i.e Good X. And then, there is a corner solution on the horizontal axis.

5. If MRS = MU_X/ MU_Y< P_X/ P_Y or MU_X/ P_X < MU_Y/ P_Y. It implies that if an additional unit of utility per dollar spending on good X is less than the additional unit of utility per dollar spending on good Y, then this means that the consumer spend his entire income on only consumption of one good i.e Good Y. There is a corner solution on the vertical axis.

6. And if MRS= MU_X/ MU_Y = P_X/ P_Y. It implies that additional unit of utility per dollar spending on good X = additional unit of utility per dollar spending on good Y, then the optimal bundle lies anywhere on the budget line/ Indifference curve .