Question

1. Suppose a perfectly competitive firm has a cost function described by

TC = 200Q + Q

2

+ 225

Each firm’s marginal revenue is $240.

a.

Find the profit maximizing level of output.

b. Is this a short-run or long-run situation? How do you know?

c.

Assuming that this firm’s total cost curve is the same as all other producers, find the long-run

price for this good.

Answer 1

Solution :-

(i)

Marginal revenue MR = $240

Total Cost = 200Q + Q² + 225

now Marginal Cost MC = 200 + 2Q

To Find maximum level of Output

MC = MR

$240 = 200 + 2Q

Now Q = 20 units

Profit is maximum at 20 units of output

(ii)

Total Cost = 200Q + Q² + 225

Average Cost = TC / Q = 200 + Q + 225/Q

Now Q = 20 units

Avg Cost = 200 + 20 + (225 / 20) = $231.25

Price is $240

For Long run equilibrium Price is equal to Avg Cost

But here Avg cost is Lower than Price

$231.25 < $240

So it is a short run situation

(iii)

To FInd the Long Run Price of Goods

Price is Equal to Avg Cost

And Price is Equal to Marginal Cost (see first part)

So Marginal cost = Avg cost for long run situation

200 + 2Q = 200 + Q + 225/Q

Q = 225 / Q

now Q² = 225

therefore Q = 15 Units

Now Price =  200 + Q + 225/Q

= 200 + 15 + 225/15

= 215 + 15 = $230

If there is any doubt please ask in comments