Competitive market prices are determined by the interplay of aggregate supply and demand; individual firms have no

Question:

Competitive market prices are determined by the interplay of aggregate supply and demand; individual firms have no control over price. Market demand reflects an aggregation of the quantities that customers will buy at each price. Market supply reflects a summation of the quantities that individual firms are willing to supply at different prices. The intersection of industry demand and supply curves determines the equilibrium market price. To illustrate this process, consider the following market demand curve where price is expressed as a function of output:

P = $40 - $0.0001Q_D (Market Demand)

or equivalently, when output is expressed as a function of price

Q_D = 400,000 - 10,000P

Assume market supply is provided by five competitors producing a standardized product (Q). Firm supply schedules are as follows:

Q₁ = 18 +2P(Firm 1)

Q₂ = 12 + 6P (Firm 2)

Q₃ = 40 + 12P (Firm 3)

Q₄ = 20 + 12P (Firm 4)

Q₅ = 10 + 8P (Firm 5)

A. Calculate the optimal quantity supplied by each firm at the competitive market prices indicated in the following table. Then, assume there are actually 1,000 firms just like each one illustrated in the table. Use this information to complete the Partial Market Supply and Total Market Supply columns.

B. Sum the individual firm supply curves to derive the market supply curve. Plot the market demand and market supply curve with price as a function of output to illustrate the equilibrium price and level of output. Verify that this is indeed the market equilibrium price-output combination algebraically.