For a perfectly competitive firm, total cost TC=300Q-20Q2+0.5Q3 a. Determine the firm's marginal cost(MC) and Average...

For a perfectly competitive firm, total cost TC=300Q-20Q²+0.5Q³

a. Determine the firm's marginal cost(MC) and Average Total Cost(ATC):

b. Determine the firm's long-run profit maximizing output and price:

c.If Price=146, what quantity will the perfect competitor produce at this price?

d. If Price=146, what is the perfect competitor's economic profit?

Expert Solution

TC=300Q-20Q2+0.5Q3
a.
MC=dTC/dQ
MC=300-40Q+1.5Q2
ATC=TC/Q
ATC=300-20Q+0.5Q2
b.
Long run price is the minimum of the ATC
To find the minimum let us find the first derivative ATC
dATC/dQ=-20+Q
Let dATC/dQ=0
Q=20
Substituting this back in ATC
ATC=300-20(20)+0.5(20*20)=100
c.
A perfectly competitive firm will produce where P=MC
146=300-40Q+1.5Q2
1.5Q2-40Q+300-146=0
1.5Q2-40Q+154=0
x=22 or 4.66
At x 22
MC=300-40(22)+1.5(22)^2=146=MR
Thus, the firm will produce 22 units.
d.
Profit=TR-TC
Profit=(Pq)-TC
Profit=(146*22)-(300*(22)-20*(22)^2+0.5*(22)^3)
Profit=968

Rahul Sunny answered 2 years ago

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