Profit Maximization Exam 3 ECON 4720

Solution to cost-minimization problem yields cost-curve 𝑐(𝑦)

• Using this curve, we can rewrite the profit maximization problem in terms of 𝑦:

max 𝜋 (𝑦) = max 𝑅 (𝑦) − 𝑐(𝑦)

marginal revenue (MR): 𝑅 ′ (𝑦)

how much revenue increases if we slightly increase output

𝑐 ′ (𝑦) marginal cost (MC):

how much total costs increase if we slightly increase output

One of the important insights in microeconomics:

At the optimal output,

marginal revenue equals marginal costs (MR = MC)

Demand curve:

total consumer demand for a product as a function of it price

Market environment:

Description of how firms respond to each other when they make their pricing and output decisions

Perfect (or pure) competition:

Each firm assumes that the market price is independent of its own level of output (price taker)

Perfectly Competitive Markets

• Many small buyers and sellers

• All firms produce identical products

• All agents have full information

• Transaction costs are negligible

• Firms can easily enter and exit the market

Competitive Markets Characteristics

– Firms and consumers are price takers

– Products are homogenous

– If a firm charges more than p* → y = 0

– Each firm faces a horizontal demand

Do we ever see PERFECTLY competitive markets?

Many markets come close, but the assumptions are very strong. Many lessons about real-life markets can be learned from a perfectly competitive mode.

Is your output always optimal if you satisfy marginal costs equals marginal revenue?

Two exceptions:

Multiple output levels satisfy this requirement

• Choose output such that MC is upward sloping

Shutdown might be better even in the short-run

• Produce only if the average cost at y* is less than the price 𝐴𝑉𝐶 (𝑦) < p

If a competitive firm’s technology exhibits DRS

the firm has a single long-run profit-maximizing production plan.

If a competitive firm’s technology exhibits IRS

• the firm does not have a profit-maximizing plan.

• IRS is inconsistent with perfect competition

If a competitive firm’s technology exhibits CRS

• They earn zero economic profit in the long run!

• If there is a positive profit more firms will come to the market and drive the price down until there is zero profit!

Relationship between cost minimization and profit maximization:

If a firm is maximizing profits then it must be minimizing costs.

Not all firms maximize

profits