Economics for Business - Lecture 3

Background to Demand

Marginal Utility Theory

• People buy goods because they derive satisfaction from them; economists call this satisfaction "utility."

• Total Utility (TU): The total satisfaction derived from all the units consumed.

• Marginal Utility (MU): The additional satisfaction derived from consuming one more unit of a good.

• MU = \frac{\Delta TU}{\Delta Q}

• The total utility (TU) curve starts at the origin and slopes upward, but only to a certain point.

• The marginal utility (MU) curve is downward sloping.

• Total utility (TU) reaches its peak when marginal utility (MU) equals zero (MU = 0).

Example of Ollie's Utility from Consuming Crisps (Daily)

• Marginal utility and the demand curve are strictly linked

• One-commodity case is trivial

• Concentrate on the multi-commodity case to see how a rational person decides what combination of goods to buy

MU and Optimum Combination of Goods

• Suppose you can buy two goods (X and Y), you have a limited amount of money (£7) and PX = PY = 1. The goods give the following marginal utilities:

  Units	MU of X	MU of Y
  1	10	8
  2	8	6
  3	6	4
  4	4	2

• If we buy 3 units of X and 4 units of Y, then TU = (10 + 8 + 6) + (8 + 6 + 4 + 2) = 44. This is not optimal.

• If we buy 4 units of X and 3 units of Y, i.e., if we choose the goods such that the MUs for X and Y are equal (to 4 in our case), then TU = (10 + 8 + 6 + 4) + (8 + 6 + 4) = 46. This is optimal.

• In monetary terms, if an individual is willing to pay £1 for an extra unit of a good, we can write MU = p. But then the optimal choice must be such that:

  • MUX = PX = MUY = PY or (MUX)(MUY)= (PX)(PY) (equi-marginal principle)

MU and Demand Curve

1. Start from the equi-marginal principle: (MUX)(MUY) = (PX)(PY)

2. For any given income, the quantity demanded for good X and for all the other goods, the equi-marginal principle must hold: this will be the first point on the demand curve.

3. Suppose now that the price of X falls. This implies that (MUX)(MUY) > (PX)(PY) i.e., you would buy more of good X and less of the others, until the principle is satisfied again: this will be the second point on the demand curve.

4. Other changes in the prices of X or other goods will determine other points on the demand curve.

Indifference Analysis

Indifference Analysis

• Marginal utility (MU) is a useful tool to study consumer choice, but utility cannot be measured in absolute terms, and we cannot really say by how much the MU of one consumer exceeds that of another consumer.

• An alternative is to use indifference analysis.

  • It does not involve measuring the amount of utility but rather ranks combinations of goods in order of preferences.

  • Ranks consumer choices using indifference curves.

Constructing an Indifference Curve

• Combinations of pears and oranges from which a consumer derives the same amount of satisfaction (utility):

  Point	Pears	Oranges
  a	30	6
  b	24	7
  c	20	8
  d	14	10
  e	10	13
  f	8	15
  g	6	20

• The consumer is indifferent between any pair of goods on the indifference curve: they all yield the same level of satisfaction.

Shapes of Indifference Curves

• Perfect Complements

• Perfect Substitutes

• Near Substitutes

• Normal

Marginal Rate of Substitution (MRS)

• Indifference curves (ICs) are usually bowed in toward the origin.

• The slope of ICs is the rate at which a consumer is willing to substitute one good for the other.

• Economists call this rate the Marginal Rate of Substitution (MRS): MRS = \frac{\Delta Y}{\Delta X}

Deriving the Marginal Rate of Substitution (MRS)

• Example:

  • Moving from point a to b: \Delta Y = 4, \Delta X = 1, MRS = 4

  • Moving from point c to d: \Delta Y = 1, \Delta X = 1, MRS = 1

• Diminishing marginal rate of substitution.

MRS and MU

• On the IC, a consumer is indifferent between any pair (bundle) of goods. In other words, along the IC, utility is constant.

• Marginal Utility: MU = \frac{\Delta TU}{\Delta Q}

• Rearranging the above equation gives: \Delta TU = MU * \Delta Q

• Suppose we have goods X and Y, and we want to know what is the change in the quantities consumed for X and Y such that the consumer remains on the same IC. We write deltaTUX + deltaTUY = 0 (or to any constant k).

• Substitute the expression obtained for \Delta TU to get: MUX deltaQX + MUY deltaQY=0QX + MUYQQY

• Rearrange to get: deltaQY/delta QX = -MUX/MUY= MRS

• The MRS between goods X and Y is equal to the ratio between their MUs.

Indifference Map

• An indifference curve shows all combinations of X and Y that give a particular level of utility.

• The further out the curve, the higher the level of utility.

• Indifference curves never intersect but move further away from the origin with increased levels of utility.

• If curve I2 is supposed to make you happier than curve I1, but they cross, then at the point of intersection, you are experiencing two different levels of utility, that is, you are both happy and happier at the same time, which makes no sense.

The Budget Line

• Indifference curves illustrate people’s preferences.

• The budget line shows the combination of goods you can buy given their prices and your income.

• Example Assumptions:

  • P_X = £2

  • P_Y = £1

  • Budget = £30

  Units of good X	0	5	10	15
  Units of good Y	30	20	10	0

Effect of a Change in Income

• An increase in income shifts the budget line outwards.

• In the prior example budget increases to £40

Effect of a Change in Price

• A fall in the price of good X rotates the budget line outwards.

• The slope of the budget line is -PX/PY. If the price of good X falls, then the absolute value of the slope becomes smaller.

The Optimum Consumption Point

• The optimum consumption point is where the budget line “touches” (is tangential to) the highest possible indifference curve.

• That is when the marginal rate of substitution equals the price ratio, i.e., MRS = MUA/MUB = PA/PB

The Effect of a Change in Income

• The income–consumption curve

• The Engel curve

Deriving an Engel Curve from an Income-Consumption Curve

• The Engel curve plots the relationship between the income level and the quantity consumed while the income-consumption curve shows how consumption changes as income varies, illustrating shifts in consumer choices across different utility levels.

The Effect of Changes in Price

• The price–consumption curve

• Deriving the individual's demand curve

Income and Substitution Effects of a Price Change

• A normal good

• Substitution effect

• Income effect