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Lecture # 07-b The Theory of Demand Lecturer: Martin Paredes. Outline. Individual Demand Curves Income and Substitution Effects and the Slope of Demand Applications: the Work-Leisure Trade-off Consumer Surplus Constructing Aggregate Demand. Individual Demand Curves.
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Lecture # 07-b The Theory of Demand Lecturer: Martin Paredes
Outline Individual Demand Curves Income and Substitution Effects and the Slope of Demand Applications: the Work-Leisure Trade-off Consumer Surplus Constructing Aggregate Demand
Individual Demand Curves Definition: The price-consumption curve of good X is the set of optimal baskets for every possible price of good X • Assumes all other variables remain constant.
Y (units) The Price-Consumption Curve PY = € 4 I = € 40 10 • PX = 4 X (units) 0 XA=2 20
Y (units) The Price-Consumption Curve PY = € 4 I = € 40 10 • • PX = 2 PX = 4 X (units) 0 XA=2 XB=10 20
Y (units) The Price-Consumption Curve PY = € 4 I = € 40 10 • • • PX = 1 PX = 2 PX = 4 X (units) 0 XA=2 XB=10 XC=16 20
Y (units) The Price-Consumption Curve PY = € 4 I = € 40 10 Price-consumption curve • • • PX = 1 PX = 2 PX = 4 X (units) 0 XA=2 XB=10 XC=16 20
Individual Demand Curves Note: • The price-consumption curve for good X can be written as the quantity consumed of good X for any price of X. • This is the individual’s demand curve for good X.
Individual's Demand Curve PX Individual Demand Curve For X • PX = 4 • PX = 2 U increasing • PX = 1 X XA XB XC
Individual Demand Curves Notes: • The consumer is maximizing utility at every point along the demand curve • The marginal rate of substitution falls along the demand curve as the price of X falls (if there was an interior solution). • As the price of X falls, utility increases along the demand curve.
Example: Finding a Demand Curve with an Interior Solution • Suppose U(X,Y) = XY • The optimal conditions are: 1. MUX = MUY Y = X PY . Y = PX . X PX PY PX PY 2. PX . X + PY . Y = I 2 PX . X = I X = I . 2 PX
PX Example: Demand Curve for an Interior Solution QD = I/(2 PX) X
Example: • Suppose U(X,Y) = X + Y • What is the price-consumption curve for good X? • What is the demand curve for good X?
Price-consumption curve: • When PX < PY, then X* = I/PX and Y* = 0 • When PX > PY, then X* = 0 and Y* = I/PY • When PX = PY, the consumer chooses any point in the budget line.
Y (units) Example: Perfect Substitutes • Y*=I/PY PX>PY IC X (units) 0
Y (units) Example: Perfect Substitutes • Y*=I/PY PX=PY IC X (units) 0
Y (units) Example: Perfect Substitutes Y*=I/PY PX<PY IC X (units) 0
Y (units) Example: Perfect Substitutes • Y*=I/PY Price-consumption curve IC X (units) 0
Demand curve for X: 0 when PX > PY QDX = {0, I/P*} when PX = PY = P* I/PX when PX < PY
PX Example: Perfect Substitutes PY I/PX Demand curve for X X 0 I/PY
Individual Demand when Income Changes Definition: The income-consumption curve of good X is the set of optimal baskets for every possible income level. • Assumes all other variables remain constant.
Y (units) Income-Consumption Curve I=40 U1 0 10 X (units)
Y (units) Income-Consumption Curve I=68 I=40 U1 U2 0 10 18 X (units)
Y (units) Income-Consumption Curve I=92 I=68 U3 I=40 U1 U2 0 10 18 24 X (units)
Y (units) Income-Consumption Curve I=92 Income consumption curve I=68 U3 I=40 U1 U2 0 10 18 24 X (units)
Individual Demand when Income Changes Note: • The points on the income-consumption curve can be graphed as points on a shifting demand curve.
Y (units) Income-Consumption Curve Income consumption curve I=40 U1 0 X (units) 10 PX $2 I=40 X (units) 10
Y (units) Income-Consumption Curve I=68 Income consumption curve U2 I=40 U1 0 X (units) 10 18 PX $2 I=68 I=40 X (units) 10 18
Y (units) Income-Consumption Curve I=92 I=68 U3 Income consumption curve U2 I=40 U1 0 X (units) 10 18 24 PX $2 I=92 I=68 I=40 X (units) 10 18 24
The Engel Curve • The income-consumption curve for good X can also be written as the quantity consumed of good X for any income level. • This is the individual’s Engel curve for good X.
I (€) The Engel Curve 40 X (units) 0 10
I (€) The Engel Curve 68 40 X (units) 0 10 18
I (€) The Engel Curve 92 68 40 X (units) 0 10 18 24
I (€) The Engel Curve Engel Curve 92 68 40 X (units) 0 10 18 24
The Engel Curve Note: • When the slope of the income-consumption curve is positive, then the slope of the Engel curve is also positive.
Definitions of Goods Normal Good: • If the income consumption curve shows that the consumer purchases more of good X as her income rises, good X is a normal good. • Equivalently, if the slope of the Engel curve is positive, the good is a normal good.
Definitions of Goods Inferior Good: • If the income consumption curve shows that the consumer purchases less of good X as her income rises, good X is a inferior good. • Equivalently, if the slope of the Engel curve is negative, the good is a normal good. Note: A good can be normal over some ranges of income, and inferior over others.
Y (units) Example: Backward Bending Engel Curve I=200 U1 • 0 X (units) 13 I (€) • 200 X (units) 13
Y (units) Example: Backward Bending Engel Curve I=300 I=200 U2 U1 • • 0 X (units) 13 18 I (€) • 300 • 200 X (units) 13 18
Y (units) Example: Backward Bending Engel Curve I=400 U3 I=300 • I=200 U2 U1 • • 0 X (units) 13 1618 I (€) • 400 • 300 • 200 X (units) 13 1618
Y (units) Example: Backward Bending Engel Curve I=400 U3 I=300 • Income consumption curve I=200 U2 U1 • • 0 X (units) 13 16 18 I (€) • 400 • Engel Curve 300 • 200 X (units) 13 16 18