Question

Columns 1 through 4 in the table at the top of the page show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are, respectively, $18, $6, $4, and $24 and that Ricardo has an income of $106.
a)What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility?

Answer 1

$$Solution$$

The above table gives the units consumed in the units column; column 1 represents the MU( marginal utility) of product A and marginal utility per dollar($\frac{MU}{P}$) of product A; column 2 represents the MU( marginal utility) of product B and marginal utility per dollar($\frac{MU}{P}$) of product B; column 3 represents the MU( marginal utility) of product C and marginal utility per dollar($\frac{MU}{P}$) of product C; column 4 represents the MU( marginal utility) of product D and marginal utility per dollar($\frac{MU}{P}$) of product D; column 5 represents the MU( marginal utility) of dollar and marginal utility per dollar($\frac{MU}{P}$).

And $\frac{MU}{P}=marginal\ utility\ per\ price\ of\ the\ product$

A consumer will be in equilibrium when he spends his given income on the purchase of different goods and services so as to maximize his total utility. Utility is maximized when $\frac{MU}{P}$ of the products are equal. In the above table we can observe that $\frac{MU}{P}$ of all the products gets equal at 2. $\frac{MU_A}{P_A}=\frac{MU_B}{P_B}=\frac{MU_C}{P_C}=\frac{MU_D}{P_D}=\frac{MU_S}{P_S}=2$ utils, gives the utility maximization purchase for Ricardo.

When,

$\frac{MU_A}{P_A}$  is equal to 2, Ricardo consumes 4 units of A;

$\frac{MU_B}{P_B}$  is equal to 2, Ricardo consumes 3 units of B;

$\frac{MU_C}{P_C}$  is equal to 2, Ricardo consumes 3 units of C;

$\frac{MU_D}{P_D}$  is lower than 2, so this product will not maximize his utility making him to consume 0 units of product D;

Hence Ricardo will purchase 4 units of A; 3 units of B; 3 units of C and 0 units of D in maximizing his utility.