The long-run cost function of a firm producing widgets in a competitive market is given by y2 + O for y = 0 where y is the quantity of widgets

Economics Dec 16, 2020

The long-run cost function of a firm producing widgets in a competitive market is given by y2 + O for y = 0 where y is the quantity of widgets. a. (6 points) Find the lowest price at which this firm will supply a positive number of widgets in the long run. What is the output of the firm at this price? b. (5 points) For the price you found in part (a), if there are 1,000 identical firms operating in this market, what would be the equilibrium market demand for widgets?

Expert Solution

In long run, a firm will produce at the point where Price = MC = ATC

MC = dc/dy = 2y

ATC = c/y = y + (10/y)

Equating MC and ATC,

2y = y + (10/y)

y = 10/y

y² = 10

y = 3.16

Minimum price = MC = 2 x 3.16 = 6.32

Equilibrium market demand = individual firm quantity x total number of firms = 3.16 x 1000 = 3,160

Archived Solution

Unlocked Solution

You have full access to this solution. To save a copy with all formatting and attachments, use the button below.

Already a member? Sign In

Important Note: This solution is from our archive and has been purchased by others. Submitting it as-is may trigger plagiarism detection. Use it for reference only.

For ready-to-submit work, please order a fresh solution below.

Or get 100% fresh solution

Get Custom Quote