# Consumer Demand Theory II

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Consumer Demand Theory II
Session 3, EA 4th July, 2007 Prof. Samar K. Datta

Overview of items intended to be covered in this session
Consumer Choice Interpretation of consumer equilibrium: Equi-marginal principle Corner solution Diminishing MU & diminishing MRS Income effect and distinction between normal and inferior goods Engel curve Price consumption curve and demand curve Substitutes and complements Examples /Food for thought 2

Two conditions for optimal consumer choice
1) Must be located on the budget line. 2) Must give the consumer the most preferred combination of goods and services (i.e., maximum satisfaction). 69

indifference curve are
Consumer Choice Pc = \$2 Pf = \$1 I = \$80 Clothing (units per week) A At market basket A the budget line and the indifference curve are tangent and no higher level of satisfaction can be attained. At A: MRS =Pf/Pc = .5 40 U2 Budget Line 30 20 20 40 80 Food (units per week) 78

Marginal utility and consumer choice
When consumers maximize satisfaction: Since MRS is also equal to the ratio of the marginal utilities of consuming F and C: 115

Marginal utility and consumer choice
The equation for utility maximization can be alternatively expressed as: 116

Marginal utility and consumer choice
Total utility is maximized when the budget is allocated so that the marginal utility per dollar of expenditure is the same for each good. This is referred to as the equal marginal principle. 117

A Corner Solution A U2 U3 U1 A corner solution exists at point B. B
Frozen Yogurt (cups monthly) A U2 U3 U1 A corner solution exists at point B. B Ice Cream (cup/month) 84

Condition for corner solution
MUX/PX > MUY/PY Implications of corner solution: brand loyalty at any price?

Questions on diminishing MU & diminishing MRS
Does diminishing MRS necessarily imply diminishing MUs? Does diminishing MUs necessarily imply diminishing MRS?

Income Changes, Income Consumption Curve, and Shift in Demand Curve
An increase in income shifts the budget line to the right, increasing consumption along the income-consumption curve. Thus, increase in income shifts the demand curve to the right. 4

Income Consumption Curve
Clothing (units per month) D 7 16 U3 Assume: Pf = \$1 Pc = \$2 I = \$10, \$20, \$30 5 10 B U2 Income-Consumption Curve An increase in income, with the prices fixed, causes consumers to alter their choice of market basket. 3 4 A U1 Food (units per month)

Income Changes & Shifts in the Demand Curve
Price of food An increase in income, from \$10 to \$20 to \$30, with the prices fixed, shifts the consumer’s demand curve to the right. 16 D3 H 10 D2 G 4 D1 E \$1.00 Food (units per month)

Normal vs. Inferior Good
Normal Good - The income-consumption curve has a positive slope: The quantity demanded increases with income. The income elasticity of demand is positive. Inferior Good - The income-consumption curve has a negative slope: The quantity demanded decreases with income. The income elasticity of demand is negative. 4

An Inferior Good 15 30 Steak (units per month) 10 5 20 Hamburger
C Steak (units per month) Income-Consumption Curve …but hamburger becomes an inferior good when the income consumption curve bends backward between B and C. 10 5 20 A U1 B U2 Both hamburger and steak behave as a normal good, between A and B... Hamburger (units per month)

Individual Demand Engel Curves
Engel curves relate the quantity of good consumed to income. If the good is a normal good, the Engel curve is upward sloping. If the good is an inferior good, the Engel curve is downward sloping. 4

Engel Curves 30 Inferior Normal 20 10 4 8 12 16 Income (\$ per month)
Engel curve is backward bending for inferior goods. Inferior Normal 20 10 Food (units per month) 4 8 12 16

Price Consumption Curve
Clothing (units per month) The price-consumption curve traces out the utility maximizing market basket for the various prices for food. 6 A Price-Consumption Curve U1 5 D B 4 U3 U2 Food (units per month) 4 12 20 4

Individual Demand Curve
Price of Food Demand Curve Individual Demand relates the quantity of a good that a consumer will buy to the price of that good. H E G \$2.00 4 12 20 \$1.00 \$.50 Food (units per month) 4

Derivation of Demand Curve from Price Consumption Curve
Clothing (units per month) Price of food

Substitutes and Complements
Two goods are considered substitutes if an increase (decrease) in the price of one leads to an increase (decrease) in the quantity demanded of the other. e.g. movie tickets and video rentals Two goods are considered complements if an increase (decrease) in the price of one leads to a decrease (increase) in the quantity demanded of the other. e.g. petrol and motor oil Two goods are independent when a change in the price of one good has no effect on the quantity demanded of the other. 4

Substitutes and Complements
If the price consumption curve is downward-sloping, the two goods are considered substitutes. If the price consumption curve is upward-sloping, the two goods are considered complements. 4

Example: College Trust Fund
Other Consumption (\$) The trust fund shifts the budget line A U1 A: Consumption before the trust fund U2 B B: Requirement that the trust fund must be spent on education C U3 C: If the trust could be spent on other goods – i.e., unconstrained P Q Education (\$) 92

Example: Gasoline Rationing
Spending on other goods (\$) 5,000 U1 C 15,000 2,000 D With a limit of 2,000 gallons, the consumer moves to a lower indifference curve (lower level of utility). 18,000 U2 B 20,000 A 20,000 Will the consumer be necessarily worse off at D? Gasoline (gallons per year) 123

Food for thought How would you display effect of income tax (proportional or progressive) with or without certain exemptions (e.g., on medical insurance)? How will commodity taxation change consumer equilibrium? How will income taxation influence labor supply? How will consumer indifference curves look like if one good is a bad, or both goods are bad? Is it possible to display exchange between two people having fixed endowments of two goods and no income, when there are no formal markets or prices to facilitate exchange?