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Fundamentals of Markets
© 2011 D. Kirschen and the University of Washington
1
Let us go to the market...
• Opportunity for buyers and
sellers to:
– compare prices
– estimate demand
– estimate supply
• Achieve an equilibrium
between supply and
demand
© 2011 D. Kirschen and the University of Washington
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How much do I value apples?
Price
One apple for my break
Take some back for lunch
Enough for every meal
Home-made apple pie
Home-made cider?
Quantity
Consumers spend until the price is equal to their marginal utility
© 2011 D. Kirschen and the University of Washington
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Demand curve
• Aggregation of the
individual demand of all
consumers
• Demand function:
Price
q = D(p )
• Inverse demand function:
Quantity
© 2011 D. Kirschen and the University of Washington
p = D-1(q)
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Elasticity of the demand
Price
High elasticity good
• Slope is an indication of the
elasticity of the demand
• High elasticity
– Non-essential good
– Easy substitution
Quantity
• Low elasticity
– Essential good
– No substitutes
Price
Low elasticity good
• Electrical energy has a very
low elasticity in the short
term
Quantity
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Elasticity of the demand
• Mathematical definition:
dq
p dq
q
e=
= ×
dp q dp
p
• Dimensionless quantity
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Supply side
• How many widgets shall I produce?
– Goal: make a profit on each widget sold
– Produce one more widget if and only if the cost of
producing it is less than the market price
• Need to know the cost of producing the next widget
• Considers only the variable costs
• Ignores the fixed costs
– Investments in production plants and machines
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How much does the next one costs?
Cost of producing a widget
Total
Quantity
Normal production procedure
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How much does the next one costs?
Cost of producing a widget
Total
Quantity
Use older machines
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How much does the next one costs?
Cost of producing a widget
Total
Quantity
Second shift production
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How much does the next one costs?
Cost of producing a widget
Total
Quantity
Third shift production
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How much does the next one costs?
Cost of producing a widget
Total
Quantity
Extra maintenance costs
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Supply curve
Price or marginal cost
• Aggregation of marginal cost
curves of all suppliers
• Considers only variable
operating costs
• Does not take cost of
investments into account
• Supply function:
p = S (q)
-1
Quantity
• Inverse supply function:
q = S(p )
© 2011 D. Kirschen and the University of Washington
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Market equilibrium
Price
Supply curve
Willingness to sell
market equilibrium
market
clearing
price
Demand curve
Willingness to buy
volume
transacted
© 2011 D. Kirschen and the University of Washington
Quantity
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Supply and Demand
Price
supply
equilibrium point
demand
Quantity
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Market equilibrium
q = D(p ) = S(p )
*
-1 *
-1 *
p = D (q ) = S (q )
*
Price
supply
market
clearing
price
demand
volume
transacted
© 2011 D. Kirschen and the University of Washington
*
*
• Sellers have no incentive
to sell for less
• Buyers have no incentive
to buy for more
Quantity
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Centralized auction
• Producers enter their bids:
quantity and price
– Bids are stacked up to
construct the supply
curve
• Consumers enter their
offers: quantity and price
– Offers are stacked up to
construct the demand
curve
• Intersection determines the
market equilibrium:
– Market clearing price
– Transacted quantity
© 2011 D. Kirschen and the University of Washington
Price
Quantity
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Centralized auction
• Everything is sold at the
market clearing price
• Price is set by the “last” unit
sold
• Marginal producer:
– Sells this last unit
– Gets exactly its bid
• Infra-marginal producers:
– Get paid more than their
bid
– Collect economic profit
• Extra-marginal producers:
– Sell nothing
© 2011 D. Kirschen and the University of Washington
Price
supply
Extra-marginal
Inframarginal
demand
Quantity
Marginal producer
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Bilateral transactions
• Producers and consumers trade directly and
independently
• Consumers “shop around” for the best deal
• Producers check the competition’s prices
• An efficient market “discovers” the
equilibrium price
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Efficient market
• All buyers and sellers have access to sufficient
information about prices, supply and demand
• Factors favouring an efficient market
– number of participants
– Standard definition of commodities
– Good information exchange mechanisms
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Examples
• Efficient markets:
– Open air food market
– Chicago mercantile exchange
• Inefficient markets:
– Used cars
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Consumer’s Surplus
• Buy 5 apples at 10¢
• Total cost = 50¢
• At that price I am
getting apples for which
I would have been
ready to pay more
• Surplus: 12.5¢
Price
15¢
Consumer’s surplus
10¢
Total cost
5
© 2011 D. Kirschen and the University of Washington
Quantity
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Economic Profit of Suppliers
Price
Price
supply
π
supply
Profit
demand
Revenue
demand
Cost
Quantity
Quantity
• Cost includes only the variable cost of production
• Economic profit covers fixed costs and shareholders’
returns
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Social or Global Welfare
Price
Consumers’ surplus
supply
+
Suppliers’ profit
= Social welfare
© 2011 D. Kirschen and the University of Washington
demand
Quantity
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Market equilibrium and social welfare
π
π
supply
Operating point
supply
Welfare loss
demand
demand
Q
Market equilibrium
© 2011 D. Kirschen and the University of Washington
Q
Artificially high price:
• larger supplier profit
• smaller consumer surplus
• smaller social welfare
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Market equilibrium and social welfare
π
π
supply
demand
Welfare loss
supply
demand
Operating point
Q
Market equilibrium
© 2011 D. Kirschen and the University of Washington
Q
Artificially low price:
• smaller supplier profit
• higher consumer surplus
• smaller social welfare
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What’s “the price”?
• Price = marginal revenue of supplier
= marginal cost of supplier
= marginal cost of consumer
= marginal utility to consumer
• Market price varies with offer and demand:
– If demand increases
• Price increases beyond utility for some
consumers
• Demand decreases
• Market settles at a new equilibrium
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What’s “the price”?
– If demand decreases
• Price decreases
• Some producers leave the market
• Market settles at a new equilibrium
• In theory, there should never be a shortage
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Price vs. Tariff
• Tariff: fixed price for a commodity
• Assume tariff = average of market price
• Period of high demand
– Tariff < marginal utility and marginal cost
– Consumers continue buying the commodity rather
than switch to another commodity
• Period of low demand
– Tariff > marginal utility and marginal cost
– Consumers do not switch from other commodities
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Concepts from the Theory of the Firm
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Production function
y = f ( x1,x 2 )
• y:
output
• x1 , x2: factors of production
y
y
x2 fixed
x1 fixed
x1
x2
Law of diminishing marginal products
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Long run and short run
• Some factors of production can be adjusted
faster than others
– Example: fertilizer vs. planting more trees
• Long run: all factors can be changed
• Short run: some factors cannot be changed
• No general rule separates long and short run
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Input-output function
y = f ( x1 ,x2 )
x 2 fixed
The inverse of the production function is the
input-output function
x 1 = g ( y ) for x 2 = x 2
Example: amount of fuel required to produce a
certain amount of power with a given plant
© 2011 D. Kirschen and the University of Washington
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Short run cost function
c SR ( y ) = w 1 × x 1 + w 2 × x 2 = w 1 × g( y ) + w 2 × x 2
• w1, w2: unit cost of factors of production x1, x2
c SR ( y )
© 2011 D. Kirschen and the University of Washington
y
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Short run marginal cost function
c SR ( y )
dc SR ( y )
Convex due to law
of marginal returns
y
dy
Non-decreasing function
y
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Optimal production
• Production that maximizes profit:
max { p × y - c SR ( y ) }
y
d { p × y - c SR ( y ) }
dy
p=
dc SR ( y )
dy
© 2011 D. Kirschen and the University of Washington
=0
Only if the price π does not depend
on y  perfect competition
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Costs: Accountant’s perspective
• In the short run, some costs are
variable and others are fixed
• Variable costs:
–
–
–
–
labour
materials
fuel
transportation
Production cost [$]
• Fixed costs (amortized):
– equipments
– land
– Overheads
• Quasi-fixed costs
– Startup cost of power plant
• Sunk costs vs. recoverable costs
© 2011 D. Kirschen and the University of Washington
Quantity
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Average cost
c( y ) = c v ( y ) + c f
AC ( y ) =
c( y)
y
=
cv ( y )
Production cost [$]
Quantity
© 2011 D. Kirschen and the University of Washington
y
+
cf
y
= AVC ( y ) + AFC ( y )
Average cost [$/unit]
Quantity
38
Marginal vs. average cost
MC
AC
$/unit
Production
© 2011 D. Kirschen and the University of Washington
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When should I stop producing?
•
•
•
•
Marginal cost = cost of producing one more unit
If MC > π next unit costs more than it returns
If MC < π next unit returns more than it costs
Profitable only if Q4 > Q1 because of fixed costs
Average cost [$/unit]
Marginal
cost
[$/unit]
π
Q1
Q2
© 2011 D. Kirschen and the University of Washington
Q3
Q4
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Opportunity cost
• Use money to grow apples or to grow cherries?
• If profit from growing cherries is larger than the profit from
growing apples, growing apples has an opportunity cost
• Use money to grow apples or put it in the bank where it
earns interests?
• Profit from growing apples must be larger than bank interest
because putting money in the bank has a lower risk
• Profit from a business must be compared against the
“normal profit”, i.e. what putting money in the bank
would bring
© 2011 D. Kirschen and the University of Washington
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Costs: Economist’s perspective
• Opportunity cost:
– What would be the best use of the money spent to make
the product ?
– Not taking the opportunity to sell at a higher price
represents a cost
• Examples:
– Use the money to grow apples or put it in the bank where
it earns interests?
– Growing apples or growing kiwis?
• Comparisons should be made against a “normal profit”
– What putting money in the bank would bring
• Selling “at cost” means making a “normal profit”
– Usually not good enough because it does not compensate for the risk
involved in the business
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