Answer to Question #226781 in Economics of Enterprise for MAN T

Question

Suppose the short run market price a competitive firm faces is Birr 9 and the total cost of the firm is: TC = 200 + Q + 0.02Q 2 . Answer the questions that follow.

(A) Calculate the short run equilibrium output and profit of the firm.

(B) Derive the MC, ATC, and AVC and calculate the values at the short run equilibrium output.

(C) Calculate the producers’ surplus at the equilibrium output.

(D) Find the output level that will make the profit of the firm zero.

Answer 1

(a)

$TC=200+Q+0.02Q^2$

Solving the above equation quadratically, we get

$Q=\frac {-1+3.87}{0.04}$

=71.75

output = 71.75

profit

profit= total revenue - total cost

total revenue =$71.75\times9=645.75$

total cost =$0.02(71.75)+71.75+200=273.185$

$\therefore$ $profit =645.75-273.185=372.565$

(b)

ATC = total costs divided by total quantity produced

$ATC=\frac {273.185}{71.75}=3.8$

AVC = Total variable cost divided by total output.

$AVC=\frac {273.185}{71.75}=3.8$

(c)

Producer surplus = Total Revenue- Total Cost

$=645.75-273.185$

$=372.565$

(d)

To make profit of the firm equal to zero,

$profit=x(9)-273.185$

$0=9x-273.185$

$x=30.35$

output = 30.35 at profit =0