Converting money values to real values

Overview

Deflating a money figure to real terms, real wages and real interest rates, and why the adjustment changes the conclusion.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Nominal gross domestic product is £2,400 billion and the gross domestic product deflator stands at 120 on a base of 100. What is real output at base-year prices, and what does the calculation remove?

   Model answer

   Real output is nominal output multiplied by 100 and divided by the deflator: 2,400 multiplied by 100 divided by 120 gives £2,000 billion. Dividing by the deflator strips out the effect of the rise in the general price level since the base year, leaving only the change attributable to the volume of goods and services actually produced. Prices are 20 per cent higher than in the base year, so £2,400 billion of current output buys what £2,000 billion would have bought then.

2. 2

   Nominal gross domestic product rises 5.2% in a year in which the deflator rises 2.4%. Calculate real growth exactly, compare it with the figure obtained by subtraction, and say whether the shortcut is acceptable here.

   Model answer

   Exactly, real growth is 1.052 divided by 1.024, which is 1.0273, so 2.73 per cent. Subtracting gives 5.2 - 2.4 = 2.8 per cent. The two differ by only 0.07 percentage points, so at rates this low the subtraction is a perfectly acceptable approximation. It works because the term that the shortcut omits is the product of the two rates, which is very small when both are small.

3. 3

   Nominal wages rise 40% in a year when prices rise 25%. What is the real change in wages, and why is subtracting the inflation rate misleading here?

   Model answer

   Dividing the wage factor by the price factor gives 1.40 divided by 1.25, which is 1.12, so real wages rose 12 per cent. Subtracting gives 40 - 25 = 15 per cent, overstating the gain by three percentage points, a quarter more than the truth. The subtraction ignores that the extra money income is itself spent at the higher prices, and the size of that omission grows with both rates, so at high inflation the division method must be used.

4. 4

   Money incomes double while prices rise by 80%. What is the real change in income, and how large is the error made by subtracting?

   Model answer

   The real factor is 2.00 divided by 1.80, which is 1.111, so real income is 11.1 per cent higher. Subtracting gives 100 - 80 = 20 per cent, which is nearly double the true figure. The approximation, which is harmless at rates of two or three per cent, becomes useless once inflation reaches these levels, and any comparison of living standards during high inflation must use the division method.

5. 5

   A worker earns £620 a week when the consumer price index stands at 116 on a base of 100. Calculate the weekly wage at base-year prices.

   Model answer

   Deflating gives 620 multiplied by 100 divided by 116, which is £534.48. The pay packet buys what £534.48 would have bought in the base year, so the worker's real wage is £534.48, and the £85.52 difference is the part of the cash figure that reflects the rise in prices.

6. 6

   A pay settlement raises wages by 3.1% in a year in which inflation is 4.4%. What happens to real wages, and what does that mean for living standards?

   Model answer

   The real factor is 1.031 divided by 1.044, which is 0.9875, a fall of 1.25 per cent. The subtraction shortcut gives -1.3 per cent, close enough at these rates. Money pay has risen but buys less than it did, so this is a real pay cut and living standards financed from earnings fall. A nominal rise is entirely consistent with a real loss, which is why pay disputes are argued in real terms.

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