A firm faces demand given by the demand function 𝑃 = −4𝑄 + 220 and the firm’s total costs are modelled by 𝑇𝐶 = 4𝑄*2+ 20Q − 12 .

Question

A firm faces demand given by the demand function 𝑃 = −4𝑄 + 220 and the firm’s total costs are modelled by 𝑇𝐶 = 4𝑄²+ 20Q − 12 .

a)What is the firm’s average cost function?

b)What is the firm’s total revenue function?

Answer 1

a) Average Total Cost is calculated by dividing Total Cost by Quantity, so we take the TC function given and divide each term by the variable Q:

TC = 4𝑄² + 20Q − 12

ATC = 4𝑄²/Q + 20Q/Q − 12/Q

Then you can simplify by canceling out the Q where you can

ATC = 4Q + 20 - 12/Q

b) Total revenue is just the Price earned per unit times the Quantity. So multiply the Price function by Q:

P = -4Q + 220

Revenue = Q * (-4Q + 220)

Then distribute the Q by multiplying it by each term:

Revenue = -4Q² + 220Q