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:

[tex]Y = 400 p[/tex]

Explanation:

Given that ;

The total cost for 100 firms is TC : [tex]2+ \dfrac{y_2}{2}[/tex]

The marginal cost of one firm will be:

[tex]MC_1 = \dfrac{\delta \ TC}{\delta y}[/tex]

[tex]MC_1 = \dfrac{\delta \ ( 2+ \dfrac{y_2}{2})}{\delta y}[/tex]

[tex]MC_1 = y[/tex]

So; Now , the marginal cost for the all 100 firms  is [tex]100 \ MC_1 = 100y = Y_1 = 100 P[/tex]

The total cost for 60 firms is [tex]TC_2 =\dfrac{y^2}{10}[/tex]

The marginal cost of one firm will be:

[tex]MC_2= \dfrac{2y}{10}[/tex]

[tex]MC_2= \dfrac{y}{5}[/tex]

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

[tex]60*MC_2 = 60 * \dfrac{y}{5}[/tex]

[tex]5*60*MC_2=60y[/tex]

[tex]300MC_2 = 60 y = Y_2 = 300P[/tex]

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

[tex]Y = Y_1 +Y_2[/tex]

[tex]Y =100p+ 300 p[/tex]

[tex]Y = 400 p[/tex]

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