Barry Haworth

University of Louisville

Department of Economics

Economics 201

### Solving for Equilibrium Price and Quantity

There are two settings where we derive equilibrium price and
quantity. The first involves a price taking (i.e. perfectly
competitive) industry, and the second involves a monopoly.
Let's consider each setting.

**A. Finding Equilibrium in a Perfectly Competitive Industry:**

- Market Demand: P = 100 - 0.5Q

- Market Supply: MC = 4Q + 50

1. Set Demand equal to Marginal Cost, and then solve for Q*:

- 100 - 0.5Q = 4Q + 50

- Q* = 11.1

2. Plug Q* into either the Demand or Supply equation, and solve
for P*:

- P* = 100 - 0.5(11.1) = 94.45

**B. Finding Equilibrium in a Monopolistic Industry:**

- Demand: P = 100 - 0.5Q

- Marginal Revenue: MR = 100 - Q

- Marginal Cost: MC = 4Q + 50

1. Set Marginal Revenue equal to Marginal Cost, and then solve
for Q*:
- 100 - Q = 4Q + 50

- Q* = 10

2. Plug Q* into the Demand equation (not MC), and solve for P*:

- P* = 100 - 0.5(10) = 95

*Note that both industries face the same Market Demand and MC
curves. However, the equilibrium price and quantities which
result from each industry are not the same. Comparing the two
outcomes, we find that perfect competition leads to lower prices
and greater output. This makes good, intuitive sense since we
expect that greater competition should keep prices down.*