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.
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