demand and supply analysis
TRANSCRIPT
EPGP
Term I
q1
p1
s1
d1
q1
p1
p2
p0
surplus
shortage
The inverse demand curve for product X is givenby: PX= 25 - 0.005Q + 0.15PY, where PX represents price in rupees per unit, Qrepresents sales in tons per week, and PY
represents selling price of another product Y inrupees per unit. The inverse supply curve ofproduct X isgiven by: PX = 5 + 0.004Q.a. Determine the equilibrium price and sales of
X. Let PY = Rupees10. b. Determine whether X and Y are substitutes or
complements.
a. Equate supply to demand to calculate Q. 25 - 0.005Q + 0.15(10) = 5 + 0.004Q 21.5 = 0.009Q Q = 2,388.9 units per week
At Q = 2,388.9, P = 25 - .005(2,388.9) + 0.15(10) = Rupees14.56 per unit.
b. Since we can solve for quantity demanded as a function of prices,
There is a direct, positive relationship between Q and PY.An increase in the price of good Y generates an increase inthe quantity demanded for good X at any value of PX, whichimplies that goods Y and X are substitutes.
005.0
PP15.0+25=Q
xy -
Percentage change in quantity demanded of a good resulting from one percent change in its price
For a linear demand curve:
q
p×
pΔ
qΔ=
p/pΔ
q/qΔ=εD
1;2
If
,0 if ;0,0 If
b
ap
qp
bpa
bp
q
bp
bpaq
2
4
4
8q
p
|ε| =∞
|ε| =-1
|ε| =0
q=8-2p
|ε| >1
|ε| <1
q
p p
qq*
p*
Infinitely elastic demand
Completely inelastic demand
Percentage change in quantity demanded of one good resulting from one percent change the prices of the other
scomplement are goods theif 0
substitute are goods theif 0
/
/
cross
cross
1
2
2
1
22
11cross
q
p
p
q
pp
Percentage change in quantity demanded
resulting from one percent change in income
goods Luxury 1>ε
goods Necessity1<ε<0
goods Inferior 0<ε
goods Normal 0>ε
Q
I×
IΔ
QΔ=
I/IΔ
Q/QΔ=ε
Income
Income
Income
Income
Income
⇒
⇒
⇒
⇒
62 66
17
15
Q
P
)PP(2/1
PP
)QQ(2/1
01
01
01
01
arc
Percentage change in quantity supplied of a good resulting from one percent change in its price
Determinants:
Ability to change output
Availability of raw materials
Time horizon (short run vs. long run)
q
p×
pΔ
qΔ=
p/pΔ
q/qΔ=εS