NOTES ON
NETWORK ECONOMICS AND THE “NEW ECONOMY”
by
Prof. Nicholas Economides
Stern School of Business
October 1999
Copyright  Nicholas Economides
2
MICROECONOMICS is about
1. Buying decisions of the individual
2. Buying and selling decisions of the firm
3. The determination of prices; market interaction
4. The quantity, quality and variety of products
5. Profits
6. Consumers’ satisfaction
There are two sides in a market for a consumption good.
DEMAND
SUPPLY
Created by consumers
Created by firms
Each consumer maximizes
Each firm maximizes its profits
satisfaction (“utility”)
↑ CONSUMPTION THEORY
↑ PRODUCTION THEORY
3
1.
We will first study consumption and later production. In the third
part of the course we will take the “demand” schedule from the
consumption analysis and the “supply” schedule from the production
analysis and put them together in a market. The price, and the quantity
exchanged will be determined in the market. We will also discuss the
performance and efficiency of markets.
CONSUMPTION ANALYSIS
2.
Goods are products or services that consumers or businesses desire.
Examples: a book, a telephone call, insurance coverage. Goods may be
directly desired by consumers or may contribute to the production of other
goods that are desired by consumers. For example a machine used in the
production of cars is desirable because it is useful in the production of
cars, although it has no direct value to a consumer. Bads are products or
services that consumers desire less of. Examples: garbage, pollution,
some telephone calls. Clearly, a good for one consumer could be a bad
for another.
4
3.
If possible, each consumer would consume a very large (infinite)
amount of each good. But, each individual is constrained by his/her
ability to pay for these goods. The limitation of total funds available to an
individual defines the budget constraint. Therefore a consumer has to
maximize his/her satisfaction while not spending more than he/she has,
i.e., without violating the budget constraint.
4.
Maximization of each consumer’s satisfaction under the budget
constraint results in optimal choices for the consumer. The choices of the
consumer define his demand for each good. The demand shows how
many units a consumer is willing to buy at various prices,
Q = Q(p)
The demand curve can also be read in the opposite way as the
willingness to pay for various quantities of the good. A typical demand
curve is shown in Figure 1.
Demand curve
$
D
P(Q)
0
Q
q
5
5.
Elasticities measure the responsiveness of quantities to prices. Price
elasticity measures the percentage change in quantity as a response to a
percentage change in price. The (own) price elasticity of demand is
e = (∆Q/Q)/(∆p/p) = (∆Q/∆p)(p/q).
Note that e < 0, and that the elasticity is not the slope of the demand
curve.
If e < -1, i.e., e > 1, the demand is elastic, i.e., highly responsive to
changes in price.
If e > -1, i.e., e < 1, the demand is inelastic, i.e., not responsive to
changes in price.
If e = -1, i.e., e = 1, the demand is called uni-elastic.
6.
The income elasticity of demand measures the responsiveness of
the quantity demanded on income changes.
eI = (∆Q/Q)/(∆I/I) = (∆Q/∆I)(I/Q).
6
If eI > 0, the good is called normal.
If eI < 0, the good is called inferior.
The cross elasticity of demand measures the responsiveness of the
demand for good X on price changes of another good, Y.
ex,py = (∆x/x)/(∆py/py).
If ex,py > 0, x and y are substitutes.
If ex,py < 0, x and y are complements.
7.
If all units are sold at the same price, the consumers who are willing
to buy at a high price benefit from the existence of consumers who are
willing to pay only a low price. All units are sold at a price equal to the
low willingness to pay. The difference between what a consumer is
willing to pay and what he actually pays is called consumers surplus.
7
8.
The total willingness to pay up to Q units is the area under the
demand up to Q units, A(Q). The actual expenditure is E(Q) = QP(Q).
The difference is consumers surplus,
CS(Q) = A(Q) - E(Q).
In Figure 2, expenditure E(Q) is double-shaded, and consumers’ surplus
CS(Q) is single-shaded. A(Q), the total willingness covers both shaded
areas.
9.
Risk and Uncertainty.
Example 1: Consider the choice between receiving $10 with certainty and
receiving $8 or $12 with probability 1/2 each. Note that both alternatives
have the same expected value of $10. The utility of the first alternative is
U(10), and the utility of the second alternative is U(8)/2 + U(12)/2.
Remember, both alternatives have the same expected monetary value of
$10, but only the first one guarantees this amount with certainty. A riskaverse person will prefer the first (riskless) alternative. This means that
Consumers’ surplus
$
= CS(Q)
= E(Q) = PQ
D
A(Q) = CS(Q) + E(Q)
P(Q)
0
Q
q
8
for a risk averse person,
U(10) > U(8)/2 + U(12)/2.
Note that, for a risk-averse person, the utility of wealth is concave. See
Figure 3. This means that the marginal utility of wealth (the utility of the
last dollar) is decreasing with wealth.
A risk-lover will prefer the second (risky) alternative, i.e., for him
U(10) < U(8)/2 + U(12)/2.
Note that, for a risk-lover, the utility of wealth is convex. See Figure 4.
This means that the marginal utility of wealth (the utility of the last dollar)
is increasing with wealth.
A risk-neutral person is indifferent between the two alternatives,
U(10) = U(8)/2 + U(12)/2.
For a risk-neutral person, the utility of wealth is a straight line. This
means that the marginal utility of wealth (the utility of the last dollar) is
Risk Averse Consumer
U
U(12)
U(10)
.5U(8)+.5U(12)
U(8)
0
8
certainty equivalent
9 10
risk premium
12
W
Risk Loving Consumer
U
U(12)
.5U(8)+.5U(12)
U(10)
U(8)
0
8
10 11
12
certainty equivalent
W
9
constant for any level of wealth.
We define the certainty-equivalent of an uncertain situation as the
amount of money x that, if received with certainty, is considered equally
desirable as the uncertain situation, i.e.,
U(x) = U(8)/2 + U(12)/2.
For a risk-averse person the certainty equivalent must be less than 10, x <
10. For a risk-neutral person x = 10, and for a risk-lover x > 10.
Example 2: Suppose that a risk-averse consumer has utility function
U(W) = log(W),
where W is her wealth and “log” is the logarithm function of base 10.
(For example, log(1) = 0, log(10) = 1, log (100) = 2, log(1000) = 3,
log(10n) = n.) Suppose that the consumer with probability 1/2 has
$1,000,000, and with probability 1/2 has $10,000. How much will she be
willing to accept with certainty in return for this uncertain situation?
10
Her utility now is
.5*log(1,000,000) + .5*log(10,000) = .5*6 + .5*4 = 3 + 2 = 5.
The certainty-equivalent is $x such that log(x) = 5, i.e., x = 100,000.
The consumer is willing to accept $100,000 with certainty in return for
her uncertain situation. Note that the certainty-equivalent x = 100,000 is
much smaller than the expected value of the uncertain situation which is
.5*1,000,000 + .5*10,000 = 505,000.
10.
Insurance. An insurance contract is called actuarially fair if it
guarantees with certainty the expected value of the wealth of the uncertain
situation it replaces. (In example 1 this expected value is $10.) A risk
averse person is willing to buy actuarially fair insurance, because his
certainty equivalent is x < 10, and he is willing to replace the uncertain
situation with anything that pays with certainty more than x. A risk
neutral agent is willing to sell actuarially fair insurance. We assume
insurance companies are risk neutral. Therefore an insurance company
11
will offer an insurance contract that pays $ 10 ≥ y with certainty. A risk
averse consumer will accept a contract that pays y ≥ x.
The insurance contract that guarantees $y with certainty usually takes the
form: “The insurance company will pay you the full $12 in case of loss
(which both parties know will happen with probability 1/2) and you pay
us a premium P.” Then the premium is P = 12 - y. Since 10 ≥ y ≥ x, we
have 12-x ≥ 12-y ≥ 2, i.e., 12-x ≥ P ≥ 2. If x = 9, premium is P = 3.
Example 3: A consumer with the same utility function has wealth from
two sources. He has $10,000 in cash, and a house worth $990,000.
Suppose that the house burns down completely with probability 1/2. (The
lot is assumed to be of no value). How much is the consumer willing to
pay for full insurance coverage?
We have found above that the certainty equivalent of this uncertain
situation is $100,000. Therefore he is willing to accept any insurance
12
contract that would leave him with wealth of at least $100,000. The
insurance contract that is just acceptable is the one that leaves him with
exactly $100,000. In insurance terms, this is a contract with coverage of
$990,000 and premium 900,000. If the house does not burn down, the
consumer has wealth of 100,000 = 1,000,000 (original wealth) - 900,000
(premium). If the house burns down, the consumer has again 100,000 =
10,000 (cash) + 990,000 (payment from the insurance company) 900,000 (premium).
13
PRODUCTION ANALYSIS
11.
Output Q is produced from inputs K (machine hours -- capital)
and L (man-hours -- labor). This is summarized by the production
function Q = f(K, L). Define the marginal productivities of capital and
labor as MPK = df/dK, and MPL = df/dL. We expect both of these to be
positive. We also expect that each marginal productivity (say MPL) is
decreasing at high usage levels of the particular input (L). See Figure 5.
We also define average productivities of labor and capital as
APL = Q/L = f(K, L)/L, APK = Q/K = f(K, L)/K.
Since marginal productivity eventually (i.e., with high use of this input)
decreases, it will eventually drive the average productivity down too.
12.
It will be assumed that the objective of firms is to maximize profits.
Profits are revenues minus costs at a certain production level, q.
Revenues are simply R(q) = pq. The costs of production of q units are
Average and Marginal Productivity
of labor
q
total
output
0
L
MP
L
AP
L
0
L1 L L3
2
L
14
the costs of the inputs K and L required to produce quantity q = f(K,
L). Therefore, the firm not only has to choose its level of output, q, but
also has to choose the required inputs, K, L. We break this maximization
problem into two parts. First we will find the best (cost-minimizing)
levels of inputs K*(q), L*(q), for any fixed level of output q. As a result
of this we will have a cost function, C(q), that shows the minimum cost
for every q,
C(q) = wL*(q) + rK*(q),
where w is the unit cost of labor, L, and r is the unit cost of capital K.
Then we will maximize profits
Π(q) = R(q) - C(q).
13.
Returns to scale. A production function exhibits constant returns
to scale (CRS) if doubling the inputs results in double output,
f(2K, 2L) = 2f(K, L).
A production function exhibits increasing returns to scale (IRS) if
15
doubling the inputs results in more than double output,
f(2K, 2L) > 2f(K, L).
A production function exhibits decreasing returns to scale (DRS) if
doubling the inputs results in less than double output,
f(2K, 2L) < 2f(K, L).
14.
Total, fixed, variable, average, and marginal costs.
Total costs:
C(q) or TC(q).
Variable costs:
V(q).
Fixed costs:
F, constant.
C(q) = F + V(q).
Average total cost:
ATC(q) = C(q)/q.
Average variable cost:
AVC(q) = V(q)/q.
Average fixed cost:
AFC(q) = F/q.
ATC(q) = F/q + AVC(q).
Marginal cost:
MC(q) = C'(q) = dC/dq
16
= V'(q) = dV/dq.
Marginal cost is the cost of production of an extra unit of output q. Since
extra production does not affect fixed cost, the increase in the total cost is
the same as the increase in the variable cost, MC(q) = dC/dq = dV/dq. An
example of per unit cost curves is shown in Figure 5a. The quantity that
corresponds to the minimum of the ATC is called minimum efficient
scale (“MES”). Decreasing average cost (q < MES) corresponds to
increasing returns to scale, and increasing average cost (q > MES) )
corresponds to decreasing returns to scale.
15.
Profit maximization. Profits generated by production level q,
Π(q), are defined as revenues, R(q), minus costs, C(q),
Π(q) = R(q) - C(q).
Typically, profits are negative for small q. They increase, reach a
maximum, and then decrease. See Figure 6. At the quantity level q* that
Average and Marginal Costs,
and Minimum Efficient Scale (MES)
MC
ATC
AVC
$
min ATC
min AVC
0
MES
q
Costs, Revenues and Profits
C
R
C, R
F
0
q
1
q*
q
2
q
TT
0
-F
q
1
q*
q
2
q
17
maximizes profits, the slope of Π(q), dΠ/dq, is zero. We know that any
q,
dΠ/dq = R'(q) - C'(q) = MR(q) - MC(q).
Therefore, at q*, marginal revenue is equal to marginal cost,
MR(q*) = MC(q*).
This condition is necessary for profit maximization.
16.
In perfect competition, no firm has any influence on the market
price. Therefore, each unit of output is sold at the same price, p.
Therefore, for a competitive firm, MR(q) = p. Each firm perceives a
horizontal demand for its output (at price p).
17.
A competitive firm chooses q* so that
p = MR = MC(q*).
See Figure 7. If the price falls below minimum average total cost, the firm
Profit Maximization
for a Competitive Firm
$
Supply
p
MC
ATC
AVC
profits
min ATC
min AVC
profits =
= R(q) - C(q) =
= q[p - ATC(q)]
Supply
0
p = MC(q* )
MES q*
q
18
closes down. Therefore the supply function of a competitive firm in the
long run is its marginal cost curve above minimum ATC. For prices
below minimum ATC, the firm supplies q = 0. In the short run, a firm
cannot recover its fixed costs (by closing down). Therefore the relevant
cost function in the short run is average variable cost, AVC. The firm's
supply function in the short run is MC above minimum AVC. It supplies
zero if p < min AVC. This means that there is a range of market prices,
between min ATC and min AVC, such that the firm will produce a
positive quantity in the short run, but will shut down in the long run.
Profits are the shaded box in Figure 7,
*
*
*
*
*
Π(q ) = R(q ) - C(q ) = q [p - AC(q )].
In a perfectly competitive industry, the supply curve of the industry is the
horizontal sum of the marginal cost curves of the industry participants.
See Figure 8.
18.
Producers surplus is the difference between the revenue of the firm
Market Supply
in Perfect Competition
$
M C=S 1
S4
ATC
S5
min ATC
D
0
q
1
4q 5q
1
1
q
19
and its variable costs,
PS(q) = R(q) - V(q).
Variable costs, V(q) can be represented by the area under the marginal
cost curve (Figure 9). V(q) is the minimum revenue a firm is willing to
accept in the short run to produce q.
Total surplus (Figure 10) is the sum of consumers and producers surplus,
TS(q) = CS(q) + PS(q).
Since consumers surplus is the area under the demand minus revenue,
CS(q) = A(q) - R(q),
total surplus is
TS(q) = A(q) - R(q) + R(q) - V(q) = A(q) - V(q).
It is maximized at the quantity qc where the marginal cost curve
intersects the demand curve.
Producers’ surplus
$
S= M C
= V(q)
= R(q)
+
= PS(q)
PS(q) = R(q) - V(q)
R(q) = pq
p
0
q
q
Total surplus
(= consumers’ + producers’ surplus)
$
D
S= M C
= V(q1 )
= A(q1 )
+
= TS(q 1)
TS(q) = CS(q) + PS(q)
CS(q) = A(q) - R(q)
PS(q) = R(q) - V(q)
TS(q) = A(q) - V(q)
0
q q
1 c
q
= Dead Weight Loss