The market demand for the product is P = 30 - 0.75Q The supply is P = 10 + 0.5Q.
ID: 1104060 • Letter: T
Question
The market demand for the product is P = 30 - 0.75Q
The supply is P = 10 + 0.5Q.
One of the firms in this market has a Total cost function as C = 200 – 3q.
Solve the below and label each answer.
(a) Equilibrium output and price
(b) Optimal q for the individual firm
(c) Profit/Loss of the firm
(d) Should the firm shut down or continue to produce and why?
(e) What would be the price under which the firm should think of shutting down and not producing and quantity in other words what would be the shutdown point? And Why shouldn’t they produce, or they should produce if the price goes below or above that point?
Explanation / Answer
Demand : P = 30 - 0.75Q
Supply : P = 10 + 0.5Q.
Total cost : C = 200 – 3q
Answer A )
Equilibrium output
Demand = Supply
30 – 0.75Q= 10+0.5Q
20 = 0.8Q
Q = 25
To find equilibrium price , substituting value of Q in demand function
P = 30 – 0.75(25)
P = 11.25
Answer B )
Optimal Q i.e. profit maximizing output
MC = MR
TC = 200 – 3q
MC = -3
TR = P.Q
(30 - 0.75Q).Q
= 30Q- 0.75Q2
MR = 30 – 1.5Q
MC = MR
30 – 1.5Q = -3
33 = 1.5Q
Q = 22
Thus Q = 22 is optimal quantity
Answer C) Profit/Loss of the firm
Qty sold = Q = 25
At equilibrium price of P = 11.25
TR = PQ = 281.25
TC = 200 – 3q
At q = 25 ,
TC = 200 – 3(25)
TC = 125
Profit = TR – TC
= 281.25 – 125
Profit = 156.25
Answer d )
Shut down point occurs when P = AVC
TC = 200 – 3q
TVC = -3q
AVC = TVC/Q = - 3
Price = 11.25 which is greater than the minimum point of AVC , hence firm does not need to shut down
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