1.The Hamilton Company is a member of a perfectly competitive industry. Like all members of the industry, its total cost function is

where TC is the firm's monthly total cost (in dollars) and Q is the firm's monthly output.

a.If the industry is in long-run equilibrium, what is the price of the Hamilton Company's product?

b.What is the firm's monthly output?

2.In 2012, the box industry was perfectly competitive. The lowest point on the long-run average cost curve of each of the identical box producers was $4, and this minimum point occurred at an output of 1,000 boxes per month. The market demand curve for boxes was

where P was the price of a box (in dollars per box) and Q_D was the quantity of boxes demanded per month. The market supply curve for boxes was

Where Q_S was the quantity of boxes supplied per month.

a.What was the equilibrium price of a box? Is this the long-run equilibrium price?

b.How many firms are in this industry when it is in long-run equilibrium?

3.Given TC = 100 + 60Q - 12Q2 + Q3, find:

a.The equations of the TVC, AVC, and MC functions.

b.The level of output at which AVC and MC are minimum, and prove that the AVC and MC curves are U-shaped.

c.Find the AVC and MC for the level of output at which the AVC curve is minimum.

4.Determine the best level of output for a perfectly competitive firm that sells its product at P = $4 and faces TC = 0.04Q3- 0.9Q2 + 10Q + 5. Will the firm produce this level of output? Why?

5.Given the following cost function: TC = 1500 + 15Q - 6Q 2 + Q3

a.Determine the total fixed cost for producing 1000 units of output and 500 units of output.

b.What is AFC at:

i.1000 units of output b)

ii.500 units of output iii.

c.Determine TVC, AVC, MC and AC at 50 units of output.