Question

The bicycle industry is made up of 100 firms with the cost curve c(q)=2+q2/2 and MC(q)=q and 80 firms with the cost curve c(q)=q2/10 and MC(q)=q/5. No new firms can enter the industry. What is the industry supply curve at prices greater than $2 ?

a. q=500p
b. q=520p
c. q=400p
d. q=300

Answer 1

The industry supply curve at prices greater than $2 is q = 145p.

Step-by-step explanation:

To determine the industry supply curve at prices greater than $2, we need to find the total quantity supplied by all the firms in the industry. The first step is to find the quantity supplied by each individual firm at a price of $2 or higher.

For the 100 firms with the cost curve c(q) = 2 + q^2/2 and MC(q) = q, we can find the level of output where MC intersects the price line of $2. At this intersection, the quantity supplied by each firm is Q = 65.

For the 80 firms with the cost curve c(q) = q^2/10 and MC(q) = q/5, we can find the level of output where MC intersects the price line of $2. At this intersection, the quantity supplied by each firm is Q = 80.

The total quantity supplied by all firms in the industry at a price of $2 or higher is the sum of the quantities supplied by the 100 firms and the 80 firms, which is 65 + 80 = 145.

Therefore, the industry supply curve at prices greater than $2 is q = 145p.

Answer 2

The industry supply curve at prices greater than $2 is q = 400p.

Step-by-step explanation:

In this scenario, the industry supply curve can be determined by adding up the quantities supplied by each firm at prices greater than $2. For the first 100 firms, the cost curve is c(q) = 2 + q^2/2 and the marginal cost curve is MC(q) = q. At a price greater than $2, each firm will choose a level of output where MR (marginal revenue) equals MC. MR = P since there is no price discrimination. Let's first calculate the quantity supplied by the first group of firms:

MR = MC = q

`q = 2 + q^2/2`

`q^2/2 - q + 2 = 0`

Solving for q, we get q = -2 or q = 4. Since the quantity can't be negative, we have q = 4. Therefore, the first 100 firms will supply a total quantity of 100 * 4 = 400 at prices greater than $2.

For the next 80 firms, the cost curve is c(q) = q^2/10 and the marginal cost curve is MC(q) = q/5. Following the same process as above, we calculate the quantity supplied by the second group of firms:

MR = MC = q/5

`q/5 = 2 + q^2/10`

`q^2/10 - q/5 + 2 = 0`
Solving for q, we get q = -5 or q = 10. Since the quantity can't be negative, we have q = 10. Therefore, the next 80 firms will supply a total quantity of 80 * 10 = 800 at prices greater than $2.

Adding up the quantities supplied by both groups, the industry supply curve at prices greater than $2 is q = 400 + 800 = 1200p. Therefore, the correct answer is option c. q = 400p.