Industrial Demand And Supply Management

1. Given;
Qd =2515−2 P∧LTC =10 q−0.2 q2 +0.004 q3
In the long run, perfect competitive industry have Average Total Cost (ATC) =Marginal
Cost (MC) =Price (P)
ATC=10 q−0.2 q2+ 0.004 q3
q
ATC=10−0.2 q+ 0.004 q2
MC= dLTC
dq =10−0.4 q+ 0.012 q2
Since ATC=MC
10−0.4 q+ 0.012q2=10−0.2 q+0.004 q2
q=25
Therefore each firm output is 25
And since MC=P
P=10−0.4 × 25+0.012 ×625=$ 7.5
∴ P=$ 7.5
Since the industry demand is given by Qd =2515−2 P
Qd =2515−2(7.5)
Qd =2500
Therefore the market output is 2500
The number of firms is given by n=Qd
q
n=2500
25 =100
There are 100 firms in the industry

2. Given;
QD=4000−10 P , q=25 , MC =$ 10
Since in the long run perfect competition P=MC, the price is $10
The market output is then;
QD=4000−100=3900 units
The number of firms is given by n=QD
q
n=3900
25 =156
There are 156 firms in the industry.
3. In a perfect competitive market, the firms are price takers. The prices of the commodities
are determined by the forces of demand and supply of the industry. There is no effect into
the perfect competition market which can be brought by individual demand and supply
because of the elasticity of the market. When there increase in price of a commodity in
the market, the demand goes down while supply goes higher and with reduction of prices,
the demand rises as the supply goes down. These forces play until an equilibrium is
reached where demand and supply are equal at a certain price. From the information
given, between 1990 and 1995 the price remain the same because people were still not
familiar with the product. As people get familiar with the product the demand rises in
1996 which facilitated the increase in price. During this period the existing suppliers were
making supernormal profits which attracted other suppliers into the market since there is
free entry and exit. Between 1998 and 2002 price decline was brought about by the
number of suppliers who were now supplying surplus in the market making the prices to
go down. After 2002, the market had established an equilibrium price where both
consumers and suppliers are willing to purchase and supply the commodity respectively
and this price was $2. (McDermott)
4. Monopolist maximises profit when MR=MC
Given;
Q=100− P
3
∴ P=300−3 Q

Hence Total Revenue;
TR=QP
TR=Q ( 300−3 Q )=300 Q−3 Q2
From above equation we can get;
MR= dTR
dQ =300−6 Q
Total Cost;
TC =30 Q+1.5Q2
∴ MC = dTC
dQ =30+3 Q
Therefore the monopolist will maximise profit at;
30+3 Q=300−6 Q
Q=30
Hence;
P=300−90=$ 210
To maximise the profit, the monopolist produce 30 units and sell them at $210
5. Given;
Q=120− P
2
∴ P=240−2Q
Hence Total Revenue;
TR=QP
TR=Q ( 240−2Q )=240 Q−2 Q2
From above equation we can get;