Question

The bicycle industry is made up of 100 firms with the long-run cost curve c(y) = 2 + (y2/2) and 60 firms with the long-run cost curve c(y) = y2/10. No new firms can enter the industry. What is the long-run industry supply curve at prices greater than $2?

Answer 1

`Y = 400 p`

Step-by-step explanation:

Given that ;

The total cost for 100 firms is TC :
`2+ (y_2)/(2)`

The marginal cost of one firm will be:

`MC_1 = (\delta \ TC)/(\delta y)`

`MC_1 = (\delta \ ( 2+ (y_2)/(2)))/(\delta y)`

`MC_1 = y`

So; Now , the marginal cost for the all 100 firms is
`100 \ MC_1 = 100y = Y_1 = 100 P`

The total cost for 60 firms is
`TC_2 =(y^2)/(10)`

The marginal cost of one firm will be:

`MC_2= (2y)/(10)`

`MC_2= (y)/(5)`

The marginal cost for all the 60 firms will now be:

`60*MC_2 = 60 * (y)/(5)`

`5*60*MC_2=60y`

`300MC_2 = 60 y = Y_2 = 300P`

Finally; the long run supply function is industry supply function and which is therefore determined as :

`Y = Y_1 +Y_2`

`Y =100p+ 300 p`

`Y = 400 p`