Question

Marcelo, Arad and Fernandez are the only consumers of Eagle Shirts which is produced by Black Shirts Factory and White
Shirts Factory. The inverse demand functions of Marcelo, Arad and Fernandes are given as P = 10 − 2Q, P = 15 −
Q
2
and
P = 5 − Q, respectively. The supply function for Black Shirts Factory is QB = −4 + 2P and the supply function for White
Shirts Factory is QW = −5 + P.
(a) Find the aggregate demand function and draw it on a graph. (8 Points)
(b) Find the aggregate supply function and draw it on a graph. (7 Points)
(c) Find the market equilibrium price and quantity when only White Shirt Factory can sell Eagle Shirts in the market.
(8 Points)
(d) Find the market equilibrium price and quantity when only Black Shirt Factory can sell Eagle Shirts in the market.
Also nd the amount of Eagle Shirts that will be bought by Marcelo, Arad and Fernandes. (12 Points)

Answer 1

a) Inverse demand function of Marcelo: P = 10 − 2Q

Inverse demand function of Arad = 15-Q/2

Inverse demand function of Fernandez: P = 5 − Q

Quantity demanded by each one of them can be found out by re-arranging the inverse demand function

Aggregate demand has been plotted in green color in figure 1

b) Aggregate supply = supply of Black Shirts Factory + supply of White Shirts Factory =  −4 + 2P - 5 + P = -9+3P

Aggregate demand has been plotted in blue color in figure 1.

c) when only White Shirt Factory can sell Eagle Shirts, market supply = - 5 + P

Equilibrium price can be found out by equating supply and demand

- 5 + P = 40-3.5P

4.5P = 45

P = 10

When P = 10 , Q = - 5 + P = -5 +10 = 5

d)  when only Black Shirt Factory can sell Eagle Shirts, market supply =  −4 + 2P

Equilibrium price can be found out by equating quantity supplied and quantity demanded

−4 + 2P = 40-3.5P

5.5P = 44

P= 8

When P = 8, Q = -4+2*8 = 8

When P = 8, Fernandez will not demand anything

Therefore, only Marcelo and Arad will demand

New Total demand = 35-2.5P

market supply =  −4 + 2P

Equilibrium price can be found out by equating quantity supplied and quantity demanded

−4 + 2P = 35-2.5P

P=8.67

At this price, quantity demanded by marcelo = 0.67 and quantity demanded by Arad = 12.67