BPUB250
Problem Set2
Due: February 89, 2012 in Class
Question 1
(a)
Student demand is now given by
Q
S
= 15010(P2)=17010P
if P
≤
17.
Total demand is given by
Q
D
= 37035P
if P
≤
8
Q
D
= 17010P
if 8<P
≤
17
To find the equilibrium price and quantity, we conjecture that the equilibrium price will
be less than 8. Then, 37035P = 65P250. We get P=6.2 and Q=153. Hence 108 burritos
are sold to students and 45 are sold to the general public.
(b)
At p=6 (before the discount)
CS(General Public) = 0.5*50*(86)=50
CS(Students)=0.5*90*(156)=405
Now the price is 6.2
CS(General Public)=0.5*45*(86.2)=40.5
CS(Students)=0.5*108*(176.2)=583.2
Change in CS(General Public) = 40.5 – 50 = 9.5
Change in CS(Students) = 583.2405 = 178.2
Change total CS =
9.5 + 178.2 = 168.7
(Note: If you are calculating the change in total CS from the market demand function, be
careful about the kink in the graph)
Question 2
(a)
Set Q
d
= Q
s
22520P = 50+35P
55P = 175
P* = 3.18, Q* = 161.36
(b)
Price elasticity of demand: (
∂
Q
d
*/
∂
P*)(P*/Q
d
*)
(
∂
Q
d
*/
∂
P*)= 20 from the demand function.
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d
= (
∂
Q
d
*/
∂
P*)(P*/Q
d
*)
= 20(3.18/161.36) = 0.39
Price elasticity of supply: (
∂
Q
s
*/
∂
P*)(P*/Q
s
*)
(
∂
Q
s
*/
∂
P*)= 35 from the supply function.
ε
s
= (
∂
Q
s
*/
∂
P*)(P*/Q
s
*)
= 35(3.18/161.36) = 0.69
Both price elasticity of demand and supply are inelastic (1<
ε
d
<0 and 0<
ε
s
<1)
Price elasticity of supply is relatively more elastic so we can expect that consumers will
suffer more if a specific tax is imposed.
(c)
With the specific tax, Q
s
’ = 50+35(p
τ
) 50+35(p2)
Set Q
d
= Q
s
’
22520P = 50+35(P2)
55P = 245
P* = 4.45, Q* = 135.9
The price consumers pay is 4.45 and the price producers receive is 2.45 (=4.452)
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 Spring '08
 Seim
 Supply And Demand, general public

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