Homework 2
Economics 503
Foundations of Economic Analysis
Assigned: Session 2
Due: Session 3
1. Suppose that the supply and demand for a product are given by the functions.
Q D  40  P
Q S  20  3  P
a. Solve for the equilibrium price and quantity.
Now suppose the government puts a $4 surcharge tax on purchasers of the good, Demand
will be a function of the price inclusive of taxes, P+tax.
Q D  40  ( P  tax)
Q S  20  3  P
b. Solve for the new equilibrium quantity and price when tax = 4. How much of the good
will be produced. How much tax will be collected? What is the after tax price charged to
consumers.
Instead, the opposition party suggests putting a $4 sales tax on producers. Supply will be a
function of the price net of taxes, P-tax.
Q D  40  P
Q S  20  3  ( P  tax)
c. Solve for the new equilibrium quantity and price when tax = 4. How much of the good
will be produced. How much tax will be collected? What is the after tax price collected
by producers.
2.
Consider a consumer buying apples and bananas using $60. Use the utility curves for
Apples and Bananas in Table 1. Calculate the optimal bundle of apples and bananas if the price
of apples is $12 and the price of bananas is $4. Fill in the following chart.
Apple
Banana
#
Utility
MUA
MUA/PA
#
Total
Utility
MUB
MUB/PB
Utility
0
1
2
3
4
5
a.
b.
c.
Find the combination that offers the highest total utility.
Calculate the marginal rate of substitution at that combination and the relative
price of bananas.
Calculate the marginal utility of apples divided by the price of apples at that
combination.
Table 1
Apple
Utility
0
1
2
3
4
5
6
0
240
460
660
840
1000
1140
ΔUtility
Δapple
240
220
200
180
160
140
Banana Utility
0
0
1
122
2
242
3
350
4
456
5
559
6
659
7
756
8
850
9
940
10
1028
11
1112
12
1192
13
1268
14
1340
15
1408
ΔUtility
Δbanana
122
120
108
106
103
100
97
94
90
88
84
80
76
72
68