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TC = 5-0.5Q + 0.001 Q2 where TC is total cost (S) and Q is output rate (units pe

ID: 1127566 • Letter: T

Question

TC = 5-0.5Q + 0.001 Q2 where TC is total cost (S) and Q is output rate (units per time period) a. b. Determine the output rate that maximizes profit or minimizes losses in the shortterm. If input prices increase and cause the cost functions to become TC = 5-0. 10Q + 0.00202 what will the new equilibrium output rate be? Explain what happened to the profit maximizing output rate when input prices were increased. 4. The market for wheat consists of 500 identical firms, each with the total cost function shown: TC = 90,000 + 0.00001 Q2 where Q is measured in bushels per year. The market demand curve for wheat is Q = 90,000,000 20,000,000P, where Q is again measured in bushels and P is the price per bushel. a. Determine the short-run equilibrium price and quantity that would exist in the market. b. Calculate the profit maximizing quantity for the individual firm. Calculate the firm's short-run profit (loss) at that quantity.

Explanation / Answer

3) a) Competitive firm takes market price as given and compares the same with its marginal cost

P = MC

0.10 = -0.5 + 0.002Q

This gives Q = 300 units

This is profit maximizing output

b) The price will still be unchanged so the new quantity is

0.10 = -0.1 + 0.004Q

This gives new Q* = 50 units

With increased cost,  profit maximizing output falls to 50.

4) a) Find the market supply from marginal cost function

MC = P = 0.00002Q

Q = 50000P

Market supply = 500Q = 500*50000P or Qs = 25,000,000P

Short run equilibrium occurs at

25,000,000P = 90,000,000 - 20,000,000P

45,000,000P = 90,000,000

P* = 2 and Q = 50,000,000

This is the equilibrium price iand quantity n the market

b) Now  profit maximizing output is 50,000,000/500 = 100,000 units and profit = TR - TC = (2*100,.000 - (90,000 + 0.00001*(100000^2) = 10000.