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

Answer:

$Y = 400 p$

Explanation:

Given that ;

The total cost for 100 firms is TC : $2+ \dfrac{y_2}{2}$

The marginal cost of one firm will be:

$MC_1 = \dfrac{\delta \ TC}{\delta y}$

$MC_1 = \dfrac{\delta \ ( 2+ \dfrac{y_2}{2})}{\delta y}$

$MC_1 = y$

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 $TC_2 =\dfrac{y^2}{10}$

The marginal cost of one firm will be:

$MC_2= \dfrac{2y}{10}$

$MC_2= \dfrac{y}{5}$

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

$60*MC_2 = 60 * \dfrac{y}{5}$

$5*60*MC_2=60y$

$300MC_2 = 60 y = Y_2 = 300P$

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

$Y = Y_1 +Y_2$

$Y =100p+ 300 p$

$Y = 400 p$