Answer to Question #246466 in Accounting for DESALEGN

Question

1.     Suppose a firm sells good X in a perfectly competitive market its per unit price is 11 birr and the total cost of producing good X is given by TC = 1/3Q³ – 3Q² 20Q + 100, then answer the following questions.

Answer 1

Solution:

a.). The level of output the firm should produce to maximize profit:

A perfectly competitive firm should produce at P = MC, in order to maximize its profits.

P = 11 birr

MC = $\frac{\partial TC} {\partial Q}$

TC = 1/3Q³ – 3Q² 20Q + 100

MC = Q² – 6Q + 20

Set MC = P

Q² – 6Q + 20 = 11

Q² – 6Q + 20 – 11 = 0

Q² – 6Q + 9 = 0

Solve for Q through quadratic function:

Q = 3 units

The firm should produce 3 units to maximize profits

b.). Determine the level of profit at equilibrium:

TP = TR – TC

TR = P $\times$ Q = 11 $\times$ 3 = 33

TC = 1/3(3³) – 3(3²) + 20(3) + 100 = 9 – 27 + 60 + 100 = 142

TP = 33 – 142 = (109)

The level of profit at equilibrium = (109)

 

c.). Total Revenue (TR) = P $\times$ Q = 11 $\times$ 3 = 33

Total Cost = 1/3(3³) – 3(3²) + 20(3) + 100 = 9 – 27 + 60 + 100 = 142

 

d.). The minimum price required by the firm to stay in the market:

This is the where P = AVC

AVC = VC/Q = 1/3Q³ – 3Q² 20Q/Q = 1/3Q² – 3Q + 20 = 1/3(3²) – 3(3) + 20 = 3 – 9 + 20 = 14

AVC = 14

The minimum price required by the firm to stay in the market = 14 birr