I appreciate all help showing how to find the answers! 1. A perfectly competitiv

Question

I appreciate all help showing how to find the answers!

1. A perfectly competitive industry has 50 identical firms producing a standardized product. The market demand for the good is P = 1,000 – 2Q, and the industry supply is
P = 100 + Q. Find the profit-maximizing price and output of each identical firm.

2. In a competitive market, there are 8 firms, each with total cost given by: TC = Q^2 +100
a. Derive the firm’s long-run supply equation and the market supply equation.
b. Market demand is given by Q = 120 - P. Determine the equilibrium price and total output in the market. What is each firm’s output and economic profit?
c. In the long-run, is the number of firms likely to increase or to decrease?

3. Demand is given by P = 1,000 – 10Q and supply by P = 400 + 20Q. Equilibrium price and

output under perfect competition are:

4. The Burr Corporation’s total cost function (where TC is the total cost in dollars and Q is quantity) is TC = 200 + 4Q + 2Q^2
a. If the firm is perfectly competitive and the price of its product is $24, what is its optimal output rate?

b. At this output rate, what is its profit?
c. Based on your answers above, should this firm shut down?

Explanation / Answer

1.First find equilibrium price and quantity by equating demand and supply equations:

1000-2Q = 100+Q,

Q= 300

P=400

Output for each firm is 300/50 = 6 units.

3.  find equilibrium price and quantity by equating demand and supply equations:

1,000 – 10Q = 400 + 20Q

600 = 30Q

Q= 20

P= 600

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