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Homework answers / question archive / 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
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?
a.
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
b.
Equilibrium market demand = individual firm quantity x total number of firms = 3.16 x 1000 = 3,160
