Final exam！

ECON 339: consumer demand 1

Consumer demand

ECON 339: consumer demand 2

Consumer demand

• Consumer equilibrium: choice of optimal bundle given income and prices – that is, given the budget set

• What happens if the budget set changes? – What causes changes in budget set?

• i)Change in income, holding prices constant

• ii) Change in one price, holding other price and income constant

• iii) Change in both prices?

• iv) Change in one price, and income?

ECON 339: consumer demand 3

i) Income effects

• Why does optimal bundle change in response to change in income?

• Recall: given “rationality”, maximizing utility requires spending all income – consuming at a point on the BL

• If income ­, with prices constant – BL shifts to the right – Points formerly on BL now strictly interior

– Former choice no longer the best

• How does composition of optimal bundle change?

ECON 339: consumer demand 4

Normal and inferior goods

• What changes to optimal bundle are possible?

• Both goods increase?

• One increases, other decreases?

• Both decrease?

• Conclusion: consumption of at least one good must increase in response to increase in income.

• Alternative phrasing: “at least one good must be normal”

• Alternative to normal good? Inferior good: quantity decreases in response to increase in

income, with prices constant

ECON 339: consumer demand 5

Income expansion path, Engel curves • Income expansion path:

– In goods (x,y) space – Curve joining optimal consumption bundles as income varies,

with prices constant – Slope reflects type of goods

• Both normal • One normal, one inferior

• Engel curve:

– In (good, income) space – plots consumption path of a particular good as income varies – Slope reflects sign of income elasticity:

– Normal good vs Inferior good

– Luxuries (income elastic) vs necessities (income-inelastic)

% %

q Y q Y q Y ∆ ∂

= ∆ ∂

ECON 339: consumer demand 6

ii) Price effects

• With 2 goods, have “own-price” effects, and “cross-price effects” – As with changes in income, quantities change because budget set

changes when one or more prices change.

• A) Own price effects:

– Holding constant income and other price(s), how does quantity demanded of one good change as its price changes?

– Properties of the demand curve for this good

– Def’n of demand curve? • Quantity demanded of a good, at each price of that good,

holding income and other prices fixed.

ECON 339: consumer demand 7

Own price effects

• Consider following experiment: 1. Initial budget set {Y, pf′, po′} - consumer chooses bundle A = - conditions satisfied by this bundle? 2. Price of food decreases to pf″ < pf ′, with income and price of other

goods constant – new budget set defined by {Y, pf″, po′} - consumer chooses bundle B = - conditions satisfied by this bundle?

ECON 339: consumer demand 8

Income and substitution effects • What has happened to budget set as price falls?

- increased in size: original optimal bundle now interior - slope of BL changed: - at original optimal bundle, no longer true that MRS = price

ratio - both these changes will alter optimal bundle - to analyse total effect, we disentangle theminto separate effects: - income effect: change in size of budget set - substitution effect: change in relative prices

ECON 339: consumer demand 9

Income & substitution effects • Given: A is original bundle, B is new • Substitution Effect: • Consider point C: on original IC (through A) where

MRS = new price ratio - Consumer indifferent between A and C - since give same utility level, “choice” between them based on

relative prices

- Movement from A to C represents substitution effect – change in quantities purchased due to changes in relative prices, with utility held constant.

- sign of subst’n effect? - decrease in unit price of food, all else constant, means relative price of food falls → substitute towards food → Δq/Δp < 0

ECON 339: consumer demand 10

Income & subst’n effects • Income Effect:

– Movement from C, on original IC, to B (optimal bundle with new prices)

– same relative price, B on higher IC – response to budget set expansion

– Sign of income effect? Depends:

• normal good • inferior good

• Net effect: Income plus substitution effect

– Slope of demand curve • Normal good: • Inferior good:

ECON 339: consumer demand 11

Cross price effects

• Change in quantity of one good in response to change in price of other good, all else constant

• In general….?

• Disaggregate into income & subst’n effects: - with 2 goods, subst’n effect: - income effect? • Complements and substitutes

ECON 339: consumer demand 12

iii) Changes in both prices?

• Change both prices, holding income constant: – Shift both slope and position of BL

• proportional change (both prices increase by 10%)? • Different increases (food up by 5%, other goods up by 2%)

• Changes in both prices and income, in same proportion

(eg, both prices and income increase by 10%) – Budget set unchanged