91Ó°ÊÓ

Meredith’s budget constraint in 1990:

F + C = 1200

From the condition of utility maximization

$$\begin{gathered} \frac{M{U}_F}{P_F}=\frac{M{U}_C}{P_C} \\ C=F \\ \sin cepricesperunitis\$1each \end{gathered}$$

Using the relation in the budget equation

F + C= 1200

C=F=600

The utility for the consumption bundle (600,600) will be:

U(F, C)=FC=360000

Now, Meredith’s budget constraint in 1990:

2F + 3C = I₂₀₀₀

from the utility maximization condition

C = F = $\frac{{\mathrm{I}}_{2000}}{5}$

Meredith’s utility doesn’t change and is the same for the year 2000 (as in 1990). From the above relation, the utility function will give Meredith’s income in 2000 as:

U(F, C)=FC=360000

$$\begin{gathered} \frac{{\mathrm{I}}_{2000}^2}{25}=360000 \\ {\mathrm{I}}_{2000}=\$3000 \end{gathered}$$

The ideal cost of living adjustment is, therefore, $1800.

The cost-of-living index represents the cost of attaining a given level of utility at current prices relative to the cost to achieve the same utility at base prices.

The ideal cost-of-living index is:

$\frac{3000}{25}=2.5$

If 100 represents the cost-of-living index for 1990, the ideal cost-of-living index in 2000 will be 250. A value of 250 represents the 150% increase in cost-of-living.

The amount of money at current-year prices that an individual requires to purchase the bundle of goods and services chosen in the base year is divided by the cost of buying the same bundle at base-year prices.

The base year (1990) consumption bundle is (600,600).

The amount of money at current year prices will be:

600 x 2 + 600 x 3 = 3000

The cost of the same bundle at base prices is $1200.

Laspeyres cost-of-living index will be:

$$\begin{gathered} \frac{\underset{}{∑}{P}_{2000}{Q}_{1990}}{\underset{}{∑}{P}_{1990}{Q}_{1990}}×100 \\ =\frac{3000}{1200}×100 \\ =250 \end{gathered}$$

The Laspeyres cost-of-living index is 250.