equilibrium quantity and price

Problem 1
In a competitive market, the market demand curve is �� = 300 − 2� and the market supply
curve is �� = 3�, where � is the price per unit of the good.
1. Use Excel to determine the quantity demanded and quantity supplied for p = $5, 10, 15, …,
100 in five-dollar increments. What are the equilibrium quantity and price? Explain your
answers!
Copy and paste your answers as follows:
Price Qd Qs
$5 . .
10 . .
. .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
95 . .
100 . .
2. Determine the equilibrium quantity and price algebraically.
3. Determine the total surplus (TS) at the equilibrium price.
4. For each price p = $5, 10, 15, …, 100 in five-dollar increments, determine the consumer
surplus (CS). How does an increase in price affect the consumer surplus?
Copy and paste your answers as follows:
Price Consumer Surplus (CS)
$5 .
10 .
.
. .
. .
. .
. .
. .
. .
. .
95 .
100 .
3. For prices p = $5, 10, 15, …, 100 in five-dollar increments, determine the producer surplus
(PS). How does an increase in price affect the producer surplus?
Price Producer Surplus (PS)
$5 .
10 .
.
. .
. .
. .
. .
. .
. .
. .
95 .
100 .
Problem 2
A perfectly competitive industry is in long-run equilibrium. Each of the identical firms has a
long-run total cost function �� = 2,500 + 100q + �!. As a result, a firm’s marginal cost
function is �� = 100 + 2�.
1. In the long-run competitive equilibrium, how much does the firm produce, and what is the
equilibrium price? (Hint: In the long-run � = �� = ���)
2. If the market quantity demanded at the equilibrium price is Q = 6,000, how many firms are in
the market?
Problem 3
Suppose the inverse demand function for a monopolistically competitive firm’s product is given
by � = 250 − ”
! � and the cost function is given by �� = 3,750 + 50� + 1.5�! so that its
marginal cost is �� = 50 + 3�.
1. Determine the monopolistically competitive firm’s marginal revenue (��) as a function of Q.
2. Determine the price and quantity when the firm’s profit is maximized. Explain!
3. Determine the maximum profit achieved by the firm.
4. Can we say that this firm is operating in the long-run or short-run equilibrium at the
equilibrium price and quantity? Explain!