Ratios, shares and proportions in economic data

Overview

Concentration ratios, dependency ratios and other proportions, and what each says about the market or population it describes.

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

   The five largest firms in a market sell 28%, 19%, 14%, 9% and 7% of total output, and the remaining 23% is spread across many small producers. Calculate the five-firm concentration ratio and say what it suggests about the structure of the market.

   Model answer

   Adding the five largest shares gives 28 + 19 + 14 + 9 + 7 = 77, so the five-firm concentration ratio is 77 per cent. Just over three-quarters of output comes from five sellers, which points to an oligopoly in which each firm is large enough for its pricing and output decisions to affect its rivals. The ratio measures how concentrated sales are and nothing else, so a high figure does not by itself prove that competition is weak.

2. 2

   A country has 1.8 million people, of whom 380,000 are aged under 16 and 310,000 are aged over 65, the rest being of working age. What is the dependency ratio, and why does a rise in it put pressure on the public finances?

   Model answer

   The working-age population is 1,800,000 - 380,000 - 310,000 = 1,110,000 and the number of dependants is 380,000 + 310,000 = 690,000. The dependency ratio is 690,000 divided by 1,110,000, which is 0.62, or about 62 dependants for every 100 people of working age. If the ratio rises there are fewer taxpayers supporting each pensioner and each child, so spending on pensions, health and education must be met from a narrower tax base, forcing higher tax rates, more borrowing or lower spending per head.

3. 3

   A firm's capital stock of £3.2 billion produces output worth £800 million a year. What is the capital-output ratio, and what would a rise in it mean for the investment needed to raise output?

   Model answer

   The ratio is 3,200 divided by 800, which is 4, usually written 4:1. It takes £4 of capital to generate £1 of annual output. If the ratio rises, each extra pound of yearly output requires more capital than before, so a given increase in output needs a larger volume of investment. That is a fall in the productivity of capital, and it makes growth more expensive in terms of forgone current consumption.

4. 4

   Government debt stands at £2,700 billion and annual gross domestic product at £2,250 billion. Express the debt as a ratio of national income and explain why economists prefer that ratio to the cash total.

   Model answer

   2,700 divided by 2,250 is 1.2, so debt is 120 per cent of gross domestic product. Scaling debt to the income out of which it must be serviced allows comparison between countries of different sizes and between years, and it strips out the effect of inflation and of the growth of the economy. A cash figure that keeps rising can still represent a falling burden if income is rising faster.

5. 5

   An economy using all its resources can produce either 200 tonnes of wheat or 500 tonnes of barley. What is the trade-off as a ratio in its simplest form, and what is the opportunity cost of one tonne of each crop?

   Model answer

   The ratio of wheat to barley is 200:500, which simplifies to 2:5. Giving up all wheat production yields 500 tonnes of barley, so one tonne of wheat costs 500 divided by 200, which is 2.5 tonnes of barley. Conversely one tonne of barley costs 200 divided by 500, which is 0.4 tonnes of wheat. Because the ratio is the same wherever the economy produces, opportunity cost is constant and the production possibility frontier is a straight line.

6. 6

   A market is worth £800m in annual sales. The five largest firms sell £240m, £180m, £120m, £60m and £40m, and the rest is shared among many small firms. Calculate the three firm and five firm concentration ratios and say what they suggest about the market.

   Model answer

   The three largest firms sell £240m + £180m + £120m = £540m, which is 540 ÷ 800 = 67.5% of the market. The five largest sell £640m, which is 80%. A three firm ratio approaching 70% points to an oligopoly in which a few firms dominate and are interdependent, and the small gap between the three firm and five firm figures shows the fourth and fifth firms add little — the concentration sits with the top three rather than being spread across five.

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