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a)A rational firm operating in a perfectly competitive market has its demand and total cost function given below.
TR=20Q-30Q2
TC=50+25Q-40Q2
Required
i) Average fixed cost function
ii) Average variable cost function
iii) Marginal cost function
iv) Profit maximizing level of output
v) Maximum Profit

Respuesta :

The average fixed cost function will be 50/Q.

How to calculate the cost?

From the information given,

TR = 20Q - 30Q²

TC = 50 + 25Q - 40Q²

The average fixed cost will be:

= Fixed cost/Quantity

= 50/Q

The average variable cost will be:

= VC/Q

= (25Q - 40Q²)/Q

= 25 - 40Q

The marginal cost function will be:

TC = 50 + 25Q - 40Q²

We'll differentiate it. This will be:

MC = 25 - 80Q

The profit maximizing level of output will be:

MR = MC

20 - 60Q = 25 - 80Q

-60Q + 80Q = 25 - 20

20Q = 5

Q = 5/20 = 0.25

The profit will be:

= TR - TC

= 20Q - 30Q² - (50 + 25Q - 40Q²)

= [(20 × 0.25 - (30 × 0.25²)] - [(50 + (25 × 0.25) - (40 × 0.25²)

= [5 - 1.875] - [50 + 6.25 - 2.5]

= 3.125 - 53.75

= -50.625

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