Christopher Makler
Stanford University Department of Economics
Econ 50: Lecture 13
What, as a society, do we produce?
Who gets what?
How do we decide?
If you were an omniscient
"social planner" in charge of everything, how would you
make these decisions?
How do billions of people
coordinate their economic activities?
What does it mean to
"let the market decide"
what to produce?
Firms face prices and
choose how much to produce
Consumers face prices and
choose how much to buy
Consumers and producers are small relative to the market
(like an individual firefly)
and make one decision: how much to buy or sell at the market price.
Equilibrium occurs when
the market price is such that
the total quantity demanded
equals the total quantity supplied
Definition 1: a situation which economic forces are "balanced"
Definition 2: a situation which is
self-replicating: \(x = f(x)\)
Transition dynamics: excess demand and supply
All forces can be in balance in different ways.
Perfect information
Homogeneous good
Lots of buyers and sellers
Free entry and exit
Part 1: Competitive Equilibrium
Part 2: Welfare Analysis
Review: Market demand and supply
Finding the equilibrium price
Model 1: Identical consumers and firms
Model 2: Different consumers and firms
Gross and net consumer surplus
Producer surplus
Model 1: Identical consumers and firms
Model 2: Different consumers and firms
Individual demand curve, \(d^i(p)\): quantity demanded by consumer \(i\) at each possible price
Market demand sums across all consumers:
If all of those consumers are identical and demand the same amount \(d(p)\):
There are \(N_C\) consumers, indexed with superscript \(i \in \{1, 2, 3, ..., N_C\}\).
Market demand curve, \(D(p)\): quantity demanded by all consumers at each possible price
Market demand sums across all consumers:
Firm supply curve, \(s^j(p)\): quantity supplied by firm \(j\) at each possible price
Market supply sums across all firms:
If all of those firms are identical and supply the same amount \(s(p)\):
There are \(N_F\) competitive firms, indexed with superscript \(j \in \{1, 2, 3, ..., N_F\}\).
Market supply curve, \(S(p)\): quantity supplied by all firms at each possible price
Price \(p^*\) is an equilibrium price in a market if:
1. Consumer Optimization: each consumer \(i\) is consuming a quantity \(x_i^*(p^*)\) that solves their utility maximization problem.
2. Firm Optimization: each firm \(j\) is producing a quantity \(q_j^*(p^*)\) that solves their profit maximization problem.
3. Market Clearing: the total quantity demanded by all consumers equals the total quantity supplied by all firms.
"Marginal benefit in dollars per unit of good 1"
\(N_C\) identical consumers, each of whom
has the Cobb-Douglas utility function
\(N_F\) identical firms produce good 1, each of which
has the Cobb-Douglas production function
Unit I: Demand for Good 1
Unit II: Supply of Good 1
and income \(m\)
and capital fixed in the short run at \(\overline K\)
1. Solve for the equilibrium price and quantity if \(\alpha = \frac{1}{4}, m = 100, N_C = 64, w = 4, \overline K = 2, N_F = 64\)
2. Solve for general formula for the equilibrium price and quantity.
pollev.com/chrismakler
1. Mathematical Identity: holds by definition
2. Optimization condition: holds when an agent is optimizing
3. Equilibrium condition: holds when a system is in equilibrium
Two consumers:
Consumer Optimization: Each consumer sets MRS = price ratio
Market Demand: Sum up individual demands for all people:
This leads to the individual demand functions:
pollev.com/chrismakler
Two firms: Subway's has \(\overline K = 2\), Togo's has \(\overline K =1\), both pay wage rate \(w = 4\).
Firm Optimization: Each firm sets P = MC
Market Supply: Sum up individual supply for all firms:
Solving for \(q_S\) and \(q_T\) gives us the firms' individual supply functions:
Let's bring our consumers and firms together!
1. Consumer Optimization: each consumer \(i\) is consuming a quantity \(x_i^*(p^*)\) that solves their utility maximization problem.
2. Firm Optimization: each firm \(j\) is producing a quantity \(q_j^*(p^*)\) that solves their profit maximization problem.
3. Market Clearing: the total quantity demanded by all consumers equals the total quantity supplied by all firms.
Note: if we go back to the individual demand
and supply functions, we get:
If you were an omniscient social planner, could you do "better"
than the price the market "chooses"?
Suppose you were in charge of the economy.
How would you answer the fundamental economic questions about a particular good?
How to produce it?
Want to produce any given quantity Q
at the lowest possible cost
Who gets to consume it?
How much to produce?
Want to distribute any given quantity Q
to the people who value it the most
Want to choose the quantity Q*
to maximize total surplus
(benefit to consumers minus costs of production)
FIRM
CONSUMER
Quasilinear utility function:
Good 2 is "dollars spent on other goods"
Total benefit (in dollars)
from \(x_1\) units of good 1:
Total cost function:
Note: variable costs only
GROSS CONSUMER'S SURPLUS
(total benefit, in dollars)
Marginal benefit,
in dollars per unit:
(also MRS, marginal willingness to pay)
TOTAL VARIABLE COST
(dollars)
Marginal cost,
in dollars per unit:
FIRM
CONSUMER
Total benefit:
Total cost:
Total welfare:
Marginal welfare from producing another unit:
TOTAL WELFARE
(dollars)
Marginal welfare,
in dollars per unit:
Total benefit to consumers minus total cost to firms
Marginal benefit to consumers minus marginal cost to firms
FIRM
CONSUMER
Maximize net consumer surplus
Maximize profits
FIRM
CONSUMER
Net benefit from buying \(Q\) units at price \(P\):
Net benefit from selling \(Q\) units at price \(P\):
Total welfare:
Marginal welfare from producing another unit:
FIRMS: SUBWAY AND TOGO'S
CONSUMERS: ADAM AND EVE
A = number of sandwiches for Adam
S = number of sandwiches produced by Subway
E = number of sandwiches for Eve
T = number of sandwiches produced by Togo's
How can we choose A, E, S, and T to maximize total benefit minus total cost
subject to the constraint that the total amount produced is the total amount consumed?
If there is a single price in the market that all consumers pay, and all producers receive, and all consumers and producers are “price takers,” then:
Every consumer sets MB = p:
Every firm set MC = p:
Every firm’s MC from the last unit produced is the same.
Cannot reduce total costs by reallocating production from one firm to another
The MB of the last unit consumed by some person
equals the MC of the last unit produced by some firm
Previously: agents took the price
"as given" (exogenous) - it was determined outside the model
Today: we endogenized
the market price by analyzing the model where it's determined