Question

A firm has the following marginal cost function:

MC(y) = 2y

and fixed costs equal to $ 16. If the price of y changes from $ 8 to $ 15 what is the change in the firm's profits?

Answer 1

Given,

MC(y) = 2y

Fixed cost = $16

Price change from $8 to $15

So,

We have to find the profit at both price level and then find the change.

We know equilibrium condition for profit maximizing firm is P = MC

Also,

Profit = Total Revenue - Total Cost

As,

Total Revenue = Price * Output

Total Cost = Fixed Cost + Variable Cost

Here we are given with MC so we can integrate it to find variable cost.

So, Let's find Variable Cost first

So, Total Cost :-

And Total Revenue :-

So,

Now, Let's see for each case :-

When Price (P) = $8

Using equilibrium condition

8 = 2y

y = 8/2

y = 4

Now, Putting P = 8 and y = 4 in the Profit function as obtained above

When Price (P) = $15

Using equilibrium condition :-

15 = 2y

y = 15/2

y = 7.5

Now, Putting P = 15 and y = 7.5 in the Profit function

So, From above we can see :-

When Price is $8 then Profit = 0

When Price is $15 then Profit = 40.25

Hence,

Change in Profit = 40.25 - 0

= 40.25