Question

A firm in a competitive market is a price taker (recall that this is true for every firm and every customer in a perfectly competitive market). For this example, the market equilibrium price is $6. The firm’s total cost (TC) function is made up of Fixed Cost (FC, which does not vary with quantity) and Variable Cost (VC, which does vary with quantity). The TC function for this firm is: TC = 10 + 2Q – 0.2Q2 + 0.01Q3 a) Find the equation for the marginal cost curve (MC). Recall that MC = TC/Q. b) Find the equation for the Average Variable Cost (AVC). Recall that AVC = VC/Q. c) Find the equation for the Average Total Cost (ATC). Recall that ATC = TC/Q. d) Find the fixed cost. Recall that Total Cost = Fixed Cost + Variable Cost. e) Find the Q at which profit is maximized. Recall that this point is where Marginal Revenue ($6, the unit price of the good) is equal to Marginal Cost (for which you found the formula in part a). f) At the profit maximizing point, find the economic revenue (TR – TC at the profit maximizing Q). g) Find the shutdown price, where the Marginal Cost curve intersects the AVC curve (MC= AVC) and the AVC curve is at its lowest point (AVC/Q = 0).

Answer 1

The TC function for this firm is: TC = 10 + 2Q – 0.2Q² + 0.01Q³

Answer:- From the above equation the fixed cost will be the constant number that is = 10

While the variable cost will be the dependent of Q and it is given by 2Q – 0.2Q² + 0.01Q³

Answer:- equation for the marginal cost curve; MC = dTC/dQ. =d [ 10 + 2Q – 0.2Q² + 0.01Q³ ] /dQ.

MC equation= Q - 0.4Q + 0.03Q²

Answer:- equation for the Average Variable Cost (AVC).

AVC = VC/Q. =[2Q – 0.2Q² + 0.01Q³]/Q

AVC = 2 – 0.2Q+ 0.01Q2

Answer:- the Average Total Cost ATC = TC/Q.

ATC=[10 + 2Q – 0.2Q² + 0.01Q³]/Q

ATC = 10/Q + 2 – 0.2Q + 0.01Q²

Answer:- We know that Total Cost = Fixed Cost + Variable Cost.

FC is fixed = 10 It is independent of Q

Answer:- Q at which profit is maximized.

Total revenue = marginal cost* quantity =6Q

Profit = Total revenue – total cost

Profit = 6Q -10 - 2Q +0.2Q² - 0.01Q³

Profit =-10+4Q+0.2Q² - 0.01Q³

For profit maximization,

d/dq(profit)=0

d/dq(-10+4Q+0.2Q² - 0.01Q³)=0

4+0.4Q-0.03Q²=0

Solving above equation, we will get

Q=-6.66 ; +20

So profit maximizing quantity is 20 units

Answer:- Economic revenue =

TR = 20*6 =120

TC=(-10+4*20+0.2*20² - 0.01*20³)=-10+80+80-80=70

Economic revenue =120-70=$50