Exercises · 4. Money and Prices

Exercises

Problems to check your understanding of this chapter. The solutions are folded away — try them yourself first.

Easy

1Easy

In an economy with ☕ coffee at $2$ , 🍞 bread at $4$ , and pay of $100$ , the coffee price alone quadruples to $8$ .

Find coffee and bread consumption, the price index, and real income.

Coffee alone at

8

— coffee falls to

6.25

cups, the index rises to

250

Show solution

Coffee always takes half of income, so quadrupling its price quarters the quantity: $x_1 = 0.5 \cdot 100 / 8 = 6.25$ cups. Bread spending is still half of income, so $x_2 = 0.5 \cdot 100 / 4 = 12.5$ loaves, unchanged.
The price index re-prices the base basket ( $25$ cups, $12.5$ loaves): $(8 \cdot 25 + 4 \cdot 12.5) / 100 = 2.5$ , an index of $250$ .
Real income is $100 / 2.5 = 40$ .
One good's price jumping alone still lifts the price level and cuts real income — a relative-price change and a level rise rolled into one.

2Medium

A country's money supply grows at $8\%$ a year, real output at $2\%$ a year, and velocity is constant.

(1) What is inflation?

(2) Where is the price level (starting at $100$ ) after $5$ years?

(3) What happens to real money balances?

Money growth

8\%

, real growth

2\%

— the price path climbs at

6\%

a year.

Show solution

(1) Inflation is money growth minus the share absorbed by real growth: $\pi = 8 - 2 = 6\%$ .
(2) Prices multiply by $1.06$ each year: $P(5) = 100 \cdot 1.06^5 \approx 133.8$ .
(3) Real balances $M / P$ grow at roughly $2\%$ a year, since money grows at $8\%$ and prices at $6\%$ — exactly, $100 \cdot (1.08 / 1.06)^5 \approx 109.8$ after $5$ years. With velocity constant, $M / P = Y / V$ , so real balances have no choice but to grow alongside real output.