Download Lecture 6: Introduction to Competitive Markets

Lecture 6: Introduction to Competitive Markets
Big Picture: The next few lectures deal with
Market Structure & Competition.
Lecture 6 - Perfect Competition – many
competitors, free entry, homogeneous product,
price-taking firms
Lectures 7, 8 - Monopoly – one seller, no entry,
market power, no strategic interaction
Lecture 9 - Oligopoly – small number of competitors, entry
costly, market power, STRATEGIC INTERACTION
Perfect Competition: Output Choice & Shut
Down Decisions by the Price Taking Firm
Competitive market:
Many small firms
Each firm is a price taker; no influence on market price
For a price taking firm, the demand curve is flat, so that
Price=Marginal Revenue (MR)=Average Revenue
P(Price)
Demand curve, p=MR=AR
q (output)
Fundamental Principle of Maximization
at a function's maximum, marginal increment is zero
Altitude
Climbing Mount
Everest
Profit
Distance
marginal increment = gradient
1
Maximizing firm
profits
Output
marginal increment = MP
For a competitive firm, optimal output choice:
price (P) = marginal cost (MC)
Mathematically, profits π = TR - TC
= PQ- TC(Q)
To maximize profits, take the derivative with respect to
quantity (recalling that the competitive firm is a price-taker,
i.e., its quantity choice has no effect on market price)
d π/dQ = P - MC
d π/dQ is simply marginal profit. Hence profit is
maximized when P - MC = 0 or P=MC.
This is a specific case of a general principle. In general, a firm
maximizes profit when marginal revenue (MR) = MC. For the
competitive firm, MR=P. Hence, P=MC is profit-maximizing.
Example
TC(q)=1000 + 50q + 10q2
Price=310
MC=50+20q
P=MC implies that optimal output is q=13.
AC=1000/q+50+10q≈257
Hence π = (P-AC)q ≈ 53*13=689
Suppose that the price had been 225 and not 310.
What would the firm have done?
MC
AC
310
257
q=13
2
Optimal output is determined by marginal cost. In
fact, MC gives the firm supply function. (A firm's
supply function is how much firm is willing to
supply at a given price.)
However, the above is only true if the firm makes
money, i.e., if price is greater than average cost.
Otherwise, it would be better for the firm shut down.
The firm's supply function is given by MC when price is
greater than min AC. For lower values of p, the supply
function is zero. Hence P>AC for firm to stay in long run.
In the short run, price has to exceed average variable
cost (AVC) , where AVC=VC/Q.
Convergence to equilibrium Step 1
A competitive firm making
profits in the SR
Price
Industry Supply & Demand
Functions
S1
AC
Price1
D
MC
Output q
Industry output Q
Convergence to equilibrium: Step 2
A competitive firm making
profits in the SR
Price
Industry Supply & Demand
Functions
S1
AC
S2
Price1
Min AC
Price2
D
MC
Output q
Industry output Q
If p > AC, then profits are positive. Entry occurs.
Industry supply expands. Price decreases.
In the long-run, p = MC =(min AC for the marginal firm).
3
Entry, Exit & Convergence to long-run equilibrium:
Basic model:
New firms will enter if they can earn economic profits.
Incumbents will exit if economic profits are
negative.
Marginal firms will earn zero economic
profits in the long run.
“Inframarginal” firms can earn positive
profits in the long run.
Example of Long Run Equilibrium (LRE)
P= 1250-2Q
TC(q)=1000 + 50q + 10q2 (cost function for each firm)
MC=50+20q
AC=1000/q+50+10q
All firms produce at q=10 (min of AC)
Price=250 in LRE (otherwise entry or exit would occur)
From demand curve, Q=500.
Hence, there will be 50 firms in the market in LRE
The Public Policy of Competitive Markets
•P=MC implies efficient allocation of resources, since
production continues up to the point (q*) where the
willingness to pay for the marginal unit equals the cost
of production
Marginal Cost (MC)
Demand
q*
4
Quantity