Income and Substitution Effects PDF

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Income and Substitution Effects Price change • The effect of a price change of either of either x₁ or x₂ on the consumer means: - First, a change in the relative price ratio. After the change of price x₁ is either cheaper or dearer - Secondly, there is a change in the consumer purchasing power • A price increase means less buying power, a price decrease means more buying power • The reaction of the consumer to the change in relative prices only is measured by the substitution effect.

Income and substitution • We hypothetically adjust the consumer’s income to restore him to the level of real income he enjoyed before the price change

• Lets assume a fall in p₁. It implies an increase in real income • We have to reduce the consumer’s income by dragging the new budget line back until it is jus tangent to the original indifference curve

Substitution Effect • The substitution effect is always negative (price and quantity consumed go in opposite directions Income Effect • The income effect can be negative (normal goods) or positive (inferior goods)

• A rise in the price of a normal good induces a negative substitution effect and a negative income effect, both of which act to reduce the demand for good.

• A rise in the price of an inferior good, however, induces a negative •

substitution effect but a positive income effect, thus the overall effect is ambiguous If, when the price of an inferior good rises, the positive income effect dominates the negative substitution effect, we have the case of a Giffen Good. That explains why the demand for a Giffen Good rises (falls) when price rises (falls)

• If the price of a product which you buy a lot of and is of inferior quality rises, • • •

your initial reaction is to substitute this product with some other But other products are much more expensive and this product is still the cheapest, so the substitution effect is minimal However, your purchasing power is less than before because of the price increase. So you buy less of other goods and more of the product which, although is now more expensive, is still the cheapest

Hicks substitution effect • When the price of good fell, we ‘varied’ the consumer’s money income to

• • •

hold his real income constant. Real income is defined as the consumer’s ability to enjoy a particular level of utility. Varying money income to keep the utility constant is known as Hicks Compensating Variation in money income (HCV) HCV allows consumer to enjoy original level of utility at the new relative price ratio.

slutsky substitution effect • An alternative definition of real income is the ability to consume not a particular

• •

level of utility but a particular bundle of goods We vary the consumer’s money income following a change in price to permit him to consumer his original bundle of goods at the new relative price ratio This is known as the Slutsky Compensating Variation (SCV) in money income

slutsky vs hicks • Hicks Substitution Effect: we need to know the exact position of the indifference curves in order to learn about the various effects of a price change - Conceptually correct, but not very applicable

• Slutsky Substitution Effect: we do not need to know anything about consumer preferences to implement it and so Slutsky’s method can be implemented - Applicable but over-compensates (look at price rise compared to Hicks)

• For small changes in price the two substitution effects are virtually identical

EXAMPLE 1: Susan’s preferences over pizza (x) and salad (y) are given by the utility function U(x,y) = xy. Price of x is £4 per unit and that of y is £1 per unit. Susan had a budget, m, of £120 Compute: i) Susan’s optimal choice

• From the MRS above: y = 4x • Budget line is 4x + y = 120 • Solving for y and x: • x* = 15 and y* = 60 (Basket A) • U(x,y) = xy ⟹ U(15, 60) = 900

ii) Calculate the income and substitution effect of a decrease in to £3 per unit

• Income and substitution effect of a decrease in x to £3 per unit • The decomposition basket has to satisfy the new tangency condition and give the same level of utility:

• Solving: x’ = 17.3 and y’ = 51.9

•

m’ = 17.3*3 + 51.9*1 = 103.8

•

The consumer is “compensated” in 103.9 — 120 = -16.2

• Calculate the final basket. Tangency condition and budget constraint: • Solving: x” = 20 and y” = 60

EXAMPLE 2: Supply of Labour: Leisure is a good; that is, more of it is better than less This means that work is bad, i.e. less work is better than more The consumer earns the wage rate w per hour of work, so that the ‘price’ of an hour of leisure is w The consumption C is ‘good’, that is, more is better

• Budget constraint: - Let’s assume the consumer has some income M (non labour income) - The consumer consumption: C = M + wL where L is the amount of labour supplied

- The budget constraint can be written: M = C — wL - Lets assume that there is a maximum amount of labour that can be supplied - Adding in each side of the budget constraint:

- Let R denote leisure: - The total amount of time available for leisure: - The amount of consumption the consumer can enjoy without working: - The budget constraint becomes:

- !We can now write. The consumption as a function of the hours of leisure:

- !If the consumer decides not work: - !If he decides not have any leisure: !

• The income effect and the substitution effect work in opposite directions, as long as it is assumed that leisure is a normal good • In the above case, the income effect partly neutralises the substitution effect, but not fully, so that as W goes up, leisure decreases • If the income effect outweighed the substitution effect then:

• At a lower wage rate, the substitution effect is stronger; if the rate increases, supply of labour increases as well

• At a higher level of wages, however, a further wage increase may well outweigh the substitution effect and the labour supply will fall • The Substitution effect states that a higher wage makes work more attractive than leisure. Therefore, supply increases • The Income effect states that a higher wage means workers can achieve a target income by working less hours. Therefore, because it is easier to get enough money they work less. This is shown on the backward-bending supply of labour.

• We can introduce over-time payments. The initial equilibrium is at point 1 where the wage line is flatter • If the individual is offered a higher over-time pay, she moves to a new equilibrium (point 2) as the wage line gets steeper and on a higher indifference curve...