Chapter 10, Problem 14P

To determine

Concept introduction:

Budget Line: It is defined as the combination of all the goods that a consumer can purchase, exhausting all his income. The formula for the budget line is:

$M=X{P}_X+Y{P}_y$

Here,

• $X$ is the quantity of good X.

• $Y$ is the quantity of good Y.

• $M$ is the total income.

• $P_x$ is the price of good X.

• $P_y$ is the price of good Y.

Marginal Utility: It is defined as the change in the total utility due to a change in an additional unit of a good. It may be diminishing, increasing, or constant.

$MU=T{U}_N-T{U}_{N-1}$ or $MU=\frac{\Delta TU}{\Delta X}$

Here,

• $MU$ is the marginal utility.

• $TU$ is the total utility.

• X is the quantity of any good.

• N is the number of goods.

Marginal Utility per dollar: It is the ratio of the marginal utility to that of the price of the good.

$\frac{MU}{\$}=\frac{MU}{P_X}$

Here,

• $\frac{MU}{\$}$ is the marginal utility per dollar.

• $P_x$ is the price of $x$

Maximizing utility in the case of two goods: It states that the equilibrium level of consumption of the two goods for a consumer is achieved when the Marginal Utility per dollar of the two goods are equal. This means that the following conditions must be fulfilled:

$\frac{M{U}_X}{P_X}=\frac{M{U}_Y}{P_Y}$

Here,

• $M{U}_X$ is the marginal utility of good X.

• $M{U}_Y$ is the marginal utility of good Y.

• $P_x$ is the price of good X.

• $P_y$ is the price of good Y.