A large number of firms selling homogenous (identical) products serve an industry. Each of the firms has the following cost structure: + 10Q + Q2, so that +2Q. The firm-level cost structure holds regardless of how many firms enter the industry. Demand for the product is given by -Q
Find the cost minimizing quantity of output for each firm and the min average cost
Describe the long run supply curve for this industry by choosing A and B in +BQ
What is the long run equilibrium price and quantity
How many firms serve this market in equilibrium
Suppose now that one of the firms - Biggie Corp - discovers/invents a new way to produce the product with a different cost structure: TC = 100 + 10Q + 0.5Q2. For Biggie, MC = 10 + Q. No other firm is able to imitate this production technology, so the other firms? costs remain unchanged. What quantity of output does this firm choose to produce? How high are Biggie?s profits?
Cost minimizing quantity of output
MC = AC
MC = 10 + 2Q
AC = 400/Q + 10 + Q
10 + 2Q = 400/Q + 10 + Q
10Q + 2Q2 = 400 + 10Q + Q2
Q2 = 400
Q = 20 units
Minimum average cost
Average cost = TC/Q
This question was answered on: Sep 18, 2020
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