Question

Explain why utility maximization subject to the budget constraint implies that the consumer purchases that basket of commodities for which

a. all income is used up.

b. the marginal rate of substitution equals the price ratio.

c. the marginal utilities per dollar of the two goods are equal.

If you use a diagram in your answer, make the diagram large and label all curves, axes, and points.

Answer 1

All income should be used up because otherwise we can't determine budget line.

B Otherwise consumer will be willing to consume less or more of quantity depending on difference between price ratio and marginal rate of substitution. If marginal rate of substitution of x for y is more than that indicated by px/py he will substitute x for y until both are equal

C otherwise consumer would allocate his budget to commodity whose marginal utility per dollar is greater. Thus will result in greater utility.