Topic 4. Utility and consumer choice

(2) Theory of consumer choice

Today’s lecture:

  • The budget line
  • Modelling consumer preferences
  • Utility maximisation
  • Income changes
  • Price changes

Essential reading:Sloman Economics Section 4.3

1. The budget line

What consumption is feasible for the consumer depends on their income and the prices of goods.

e.g. In a ‘2 good world’;

1The total income to be spent on bananas and magazines is £10 per week.

2The price of a magazine is £1

3The price of a bunch of bananas is £2

The consumer can choose to:

  • buy 10 magazines and no bananas

or

  • 5 bunches of bananas and no magazines

or

  • some combination of bananas and magazines.

All possible consumption possibilities form the budget line

The budget line

  • Horizontal intercept = Income/Pmagazines
  • Vertical intercept = Income/ Pbananas
  • Slope = Pmagazines/ Pbananas

2. Budget line: changes in price

  • An increase in the price of one good causes the budget line to rotate in.
  • A decrease in the price of one good causes the budget line to rotate out.

e.g.

3. Budget line: changes in income

  • An increase in income shifts the budget line out.
  • A decrease in income shifts the budget line in.

e.g. an increase in the consumers income from £10 to £20 per week:

Budget lines show the ‘bundles’ of goods between which consumers can choose, given their income and the prices of goods. Which feasible ‘bundle’ will maximise their utility?

4. Preferences

5. Indifference curves

Marginal rate of substitution:

The amount of bananas that must be given up if the consumer receives one more magazine, in order for utility to remain the same.

MRS = Δbananas/ Δmagazines

  • MRS falls as we move along the indifference curve. Thisis related to the principle of diminishing marginal utility.

  • Utility at point a = utility at point b
  • Utility sacrificed by ‘giving up’ 2 units of Y = utility gained by getting one extra unit of X
  • MU of X must be 2 times as great as the MU of Y
  • MRS = MuX/MUY = slope of the indifference curve

6. Indifference maps

  • Ordinality
  • An IC further out from the origin = more utility
  • Utility is equal along any one IC

7. Differences in preferences

8. Maximising utility

  • Points a, bc are feasible for the consumer.
  • Point b gives more utility than points a or c.
  • Point d would give higher utility than b, but is not feasible.

The consumer chooses 2 bunches of bananas at £2 each, spending £4 on bananas, plus 6 magazines at £1 each, spending £6 on magazines and spending a total of £10 overall - the total income.

Utility is maximised where

  • MRS = PX/PY

MRS = MuX/MuY, therefore…

  • PX/PY = MuX/MuY
  • MUX/PX = MUY/PY

[the same ‘rule’ we derived in the last lecture]

9. Change in income

  • The consumer buys more of both bananas and magazines

10. Change in price

  • The consumer buys more of both bananas and magazines.
  • Why?

Next lecture: decomposing the effects of a price change into income and substitution effects.

Test your understanding…

Explain why an individual’s indifference curves cannot cross.

Test your understanding…

Sketch a person’s indifference map for two goods X and Y. Mark the optimum consumption point. Now illustrate the following (use separate diagrams for each)

(a)A rise in the price of good X but not change in the price of good Y.

(b)A shift in the person’s tastes from good Y to good X

(c)A fall in the person’s income.

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ITME no 7.doc