Consumer Demand Theory
Utility and Indifference Curves
1 Total Utility and Marginal Utility
From the total utility schedule below:
Derive marginal utility.
Graph TU and MU and indicate the saturation point with a STAR.
(Recall: TU is on the vertical axis and Qx is on the horizontal axis.)
Qx TUx
0 0
1 7
2 13
3 18
4 22
5 25
6 27
7 28
8 28
9 27
2 TU and MU
From the TU schedule below:
Derive the MU schedule.
Plot TU and MU and indicate the saturation point.
Insert trend lines and equations on each of curves.
Qy 0 1 2 3 4 5 6 7
TUy 0 4 14 20 24 26 26 24
Indifference Curves
3 The following table gives points for 4 indifference curves for a consumer.
Use Excel to plot the 4 indifference curves.
List the properties of indifference curves.
1 2 3 4
Qx Qy Qx Qy Qx Qy Qx Qy
2 13 3 12 5 12 7 12
3 6 4 8 5.5 9 8 9
4 4.5 5 6.3 6 8.3 9 7
5 3.5 6 5 7 7 10 6.3
6 3 7 4.4 8 6 11 5.7
7 2.7 8 4 9 5.4 12 5.3
4 Budget Line
Suppose the price of good Y is $1 and the price of good X is $2 per unit. Let income M = $16.
Write the budget line equation.
Graph the equation of your budget line.
Indicate the Qy and Qx at each of the axis intercepts of the budget line.
Indicate the slope of the budget line.
5 Graphical Analysis
If the consumer’s tastes and preferences are given by the indifferences from Q3 and the total income
and price constraints are given by the budget line Q5, then plot the equilibrium point for the consumer.
Consumer equilibrium:
This is where the slope of the indifference curve and slope of the budget line are equal.
6 Budget Line
A consumer enjoys both music and spaghetti.
The consumer’s income is $240 week. Music costs $12
per unit, and spaghetti costs $8 per meal.
A. Graph the budget constraint faced by the consumer.
B. If the consumer wants all music, calculate how much music they can purchase.
C. If the consumer spends half their income on music and half their income on spaghetti, how much of each good
can this consumer buy?
D. Suppose that a hoiday bonus raises income temporarily to $360. Draw the new budget constraint.
E. Indicate how many music units and spahetti dinners the consumer can buy with an income of $360.
7 Consumer Choice Theory
Suppose that a consumer consumes only about coffee and bagels.
This consumer’s utility fucntion is U =C*B, where C = number of cups of coffee daily,
B= number of bagels this consumer eats daily. The price of coffee is $3, and the price of bagels is $1.50.
The budget is $6 daily to be used for coffee and bagels.
A. What is the objective function?
B. What is the constraint?
8 Bundle Qty X Qty Y
A 2 2
B 10 0
C 1 5
D 3 2
E 2 3
D. Graph the utility function, U =X*Y.
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