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

qq

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

QQ

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