Suppose the supply curve for pizza is given by Q^S = 2P, where Q^S is the quanti
ID: 1132155 • Letter: S
Question
Suppose the supply curve for pizza is given by Q^S = 2P, where Q^S is the quantity offered for sale when the prices is P. Also, suppose the demand curve for pizza is given by Q^D = 80-3PI, where Q^D is the quantity of pizza demanded when the price is P and the level of income is I.
a.) Find the equilibrium P and Q when I = 6.
b.) Find the price-elasticity of demand at the equilibrium when I = 6, and give an interpretation in terms of percents and classify the elasticity (elastic or inelastic).
c.) Find the income-elasticity of demand at the equilibrium when I = 6, and give an interpretation in terms of percents. What type of good is this (normal, inferior, luxury).
d.) Find the equilibrium P and Q as a function of I.
e.) Find the price elasticity of demand as a function of P and I and determine when this is unitary elastic.
f.) Find the income-elasticity in terms of P and I.
Explanation / Answer
a.
Qd =Qs
80-3*P*6 = 2P
80-18P = 2P
80 = 20P
P = 80/20 = 4
Qs = 2P = 2*4 = 8
b.
P
Qd
Qs
% change in P
% change in Q
Ed
0
80
0
1
62
2
2
44
4
1.00
-0.29
-0.29
3
26
6
0.50
-0.41
-0.82
4
8
8
0.33
-0.69
-2.08
5
-10
10
0.25
-2.25
-9.00
6
-28
12
0.20
1.80
9.00
7
-46
14
0.17
0.64
3.86
8
-64
16
0.14
0.39
2.74
9
-82
18
0.13
0.28
2.25
10
-100
20
0.11
0.22
1.98
The price-elasticity of demand is elastic as the Ed = -2.08. In terms of percent, 33 percent increase in price leads to 69 percent decrease in quantity.
c.
P
Qd
Qs
% change in I
% change in Q
Ed
4
20
8
4
8
8
0.20
-0.60
-3.00
It is a normal good
d.
Qd = 80-3PI
P =(80-Qd)/3I
Qs = 2P
P = (80-Q)/6I
P
Qd
Qs
% change in P
% change in Q
Ed
0
80
0
1
62
2
2
44
4
1.00
-0.29
-0.29
3
26
6
0.50
-0.41
-0.82
4
8
8
0.33
-0.69
-2.08
5
-10
10
0.25
-2.25
-9.00
6
-28
12
0.20
1.80
9.00
7
-46
14
0.17
0.64
3.86
8
-64
16
0.14
0.39
2.74
9
-82
18
0.13
0.28
2.25
10
-100
20
0.11
0.22
1.98
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