Find the average cost function

Reference no: EM132385501

Assignment -

All firms are identical in this industry. Each firm's total cost function is given by

C(q) = ½q² - 10q + 200

a) Find the average cost (AC) function. At what level of output, q, is average cost at its lowest? [Hint: find ∂AC/∂q = 0.] And what is the value of the minimum average cost?

b) Find the marginal cost (MC) function. What is the value of MC at the lowest point of the average cost curve? In a long run equilibrium, what must be the equilibrium output and price of the typical firm and (briefly) explain why?

c) Derive the individual firm's supply curve; that is, its output, q, as a function of price, P. [Hint: recall that firms choose that level of output where P = MC.]

d) Suppose that Market Demand is Q^D = 1500 - 50P. What is the total market output sold in long run equilibrium? How many firms are there in long run equilibrium?

e) Using the number of firms found in part d), derive the industry short run supply function. [Hint: industry supply is Q^S = Nq, where N is the number of firms and q the supply function per firm. You need to find Q^S as a positive function of P.]

f) Draw the industry supply and market demand curves and point out the long run equilibrium price and industry quantity.

g) Now suppose that Market Demand permanently increases to Q^D = 2000 - 50P. Holding the industry supply curve constant (or more specifically, holding the number of firms constant), what is the new equilibrium price and industry quantity? How much does each firm produce?

h) What happens in the long run? Is there entry or exit?

i) Assume the industry is one of constant cost. Find the new long run equilibrium price, industry quantity, and quantity produced per firm. How many firms are there in the new long run equilibrium?

j) Draw the new market demand and new industry supply curves on your diagram from part f), and show the new equilibrium point, and trace the long pm expansion path.

Reference no: EM132385501

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