Unformatted text preview: Sole Propietorships
Owned/run by single individual
Owner may manage firm
Partnerships
Jointly owned and controlled
by two or more people.
Operate under partnership
agreement
If any partner leaves,
agreement dissolves
Unlimited Liability Corporation
Owned by shareholders in
proportion to ownership of
shares
Elect board of directors to run
firm
Board of directors hire
manager Limited Liability Maximize profits
=RC
Socially / environmentally / ethically conscious firms:
Maximize profits
Subject to certain constraints (limit pollution, etc.) View of firms as black box that transforms inputs into
output
Ignore questions of information / organization / coordination
These agency issues are at the core of econ / finance electives [Perloff, Ch. 6, p. 172]
The production function specifies the maximum amount of an output
that can be produced from a particular combination of inputs.
q = f(L,K)
where q units of output are produced using L units of labor and K
units of capital.
Efficient production is necessary for profit maximization, but not
sufficient. What is L?
Unskilled labor
Skilled labor
Management
May often wish to separate these, but to keep things simple, will
group together What is K?
Longlived inputs
Land
Buildings
Equipment In long run, all inputs can be adjusted
“In the long run, we’re all dead.” – Keynes In short run, only one input can be adjusted
Typically easier to adjust labor rather than capital
Cheaper and easier to hire and fire than to buy / sell new building Will look at case where capital is fixed at K Examples:
1. q = min{ L, K }
2. q = L + K
3. q = ALaKb (CobbDouglas)
a) q = L1/2K1/2 (A = , a = , b = )
b) q = L
c) q = K Suppose q = L1/2K1/2
If K = 4, q =
To produce quantity, q,
LSR(q,4) = ? Suppose q = ALaKb
LSR (q, K) = ? Suppose q = L + K
If K = 10, q =
LSR (q, 10) = Suppose q = min { L, K}
If K = 10, q =
LSR (q, 10) = MPL = ∂f ( L, K )
∂L is the change in total output resulting from using an extra unit of
labor, holding all other factors fixed.
e.g., in discrete setting,
L 1 2 3 4 q 3 6 8 9 MPL 3 3 2 1 q = L1/2K1/2; suppose K = 1.
MPL APL 3.5 3 2.5 Output 2 1.5 1 0.5 0
0 1 2 3 4 5
Labor
Total Product 6 7 8 9 10 3.5 3 2.5 Output 2 1.5 1 0.5 0
0 1 2 3 4 5 6 7 8 9 10 6 7 8 9 10 Labor
Total Product 3.5 3 2.5 Output 2 1.5 1 0.5 0
0 1 2 3 4 5
Labor Total Product Average Product 3.5 3 2.5 Output 2 1.5 1 0.5 0
0 1 2 3 4 5 6 7 8 9 Labor
Total Product Average Product Marginal Product q = L + 12L2 – L3
MPL APL 10 300 250 Output 200 150 100 50 0
0 1 2 3 4 5 6 7 8 5 6 7 8 Labor
Total Product 60 50 Output 40 30 20 10 0
0 1 2 3 4
Labor Average Product Marginal Product If MPL > APL, then APL is rising
If MPL < APL, then APL is falling
If MPL = APL, then APL is staying constant
Simple idea:
Michael Jordan had an average of 30 points per game
If he scores 35 points in the next game, increases average
If he scores 25 points in the next game, decreases average
If he scores 30 points in the next game, average remains same Works with your GPA
In quarter where GPA is higher than earlier average, pulls up GPA
In quarter where GPA is lower than earlier average, pulls down GPA
In quarter where GPA is same as earlier average, no change. The Law of Diminishing Marginal Returns states:
if a firm keeps increasing an input,
holding all other inputs and technology fixed
corresponding increases in output will become smaller eventually.
MPL is decreasing in L ∂MPL
<0
∂L Now suppose that K and L are variable
Provides greater flexibility
Production function
q = f(L, K)
e.g., q = L0.5 K0.5 Specifies possible combinations of inputs that will
produce a given level of output
q = f(L,K)
Suppose q = L0.5K0.5 = 1; what are pts on the isoquant?
L = 1, K = ?
L = 2, K = ?
L=½,K=?
L = ?, K = 3
L = ? , K = 1/4 Similar concept to indifference curves
Indifference curves hold utility constant
Isoquants hold production constant Farther isoquant is from origin, greater level of production
Isoquants do not cross
Isoquants slope downwards
Isoquants are thin lines q = min {L, K} q = min { L, K }
At efficient point,
L= K=
So slope of efficient line is / K α
L
β K q= K+ L L
Does this technology have diminishing marginal returns? Slope of isoquant indicates how one input can be substituted for
another
MRTS indicates
while holding output constant
how many units of capital can be substituted
by additional unit of labor Intuition
Suppose MPL = 1, MPK = 1/4, and you were producing 6 units
If you hire additional worker,
Increases production by MPL = 1
So output goes up by 1 Have to decrease capital to keep output same
Decrease one unit of capital, output goes down by MPK = 1
So have to decrease _ units of capital dK
= − MPL
dL
dK
MPL
MRTS =
=−
dL
MPK
MPK K q= K+ L=1 L
Can calculate slope using standard ways K q= K+ L=1 L
MPK = , MPL =
MRTS =  / q = ALa Kb
MPL =
MPK =
MRTS = Typically assume that MRTS is diminishing i.e.,
∂
 MRTS < 0
∂L This is equivalent to isoquants being convex Sufficient condition:
MPL is decreasing in L and MPK is increasing in L MP tells us what happens when one input is increased
holding others fixed
What if all inputs are increased in a proportional way?
E.g., if you double the # of inputs, do you
increase output by more than 2? (Increasing Returns to Scale)
increase output by exactly 2? (Constant Returns to Scale)
increase output by less than 2? (Decreasing Returns to Scale) Suppose >1 Decreasing Returns to Scale: f( L, K) < f(L,K)
Increasing Returns to Scale: f( L, K) > f(L,K)
Constant Returns to Scale: f( L, K) > f(L,K) Suppose f( L, K) = x f(L,K), for all > 1. a) When would f have CRS? b) When would f have Decreasing RS? c) When would f have Incr. RS? Theory of Production
Isoquants:
Combination of inputs necessary to make a fixed level of output
Slope of isoquant = Assume Diminishing MRTS Economies of Scale Explicit Costs Opportunity Costs Direct outofpocket payments
for inputs Value of best alternative use of
resource Wages, Salaries If input is owned, opportunity
cost can be measured by price
at which input could be sold Cost of capital, depreciation Total Cost = Fixed Cost + Variable Cost
Fixed Cost
Cost of inputs whose use does not vary with output level
Price of land, large machinery Variable Cost
Production expense that varies with output
Cost of labor and materials Example: Taxicab service JetBlue: New planes, leather seats, live satellite TV
Bring “humanity back to air travel”; instead of packing them like sardines. Costs
Variable Costs:
Labor: Flight attendants, ground crew, ticket counter staff, pilots
Jet fuel Fixed Costs:
10 year lease with Port Authority of New York for Terminal 6 at JFK
Salary contracts for CEO and managers
Cost of planes (unless planes are leased with optout clauses) Assume capital is fixed
C(q) = VC(q) + F Marginal cost (MC) is cost change if firm produces one more unit of
output Average cost (AC) is total cost per unit
Average variable cost (AVC) is variable cost per unit
Average fixed cost (AFC) is fixed cost per unit F = 100, VC(q) = q2 + 10q
MC: AVC: AFC: AC: F = 450, VC(q) = 100q 4q2 + 0.2q3
MC: AVC: AFC: AC: Cost of using L units of labor = wL
Suppose capital is fixed at K.
VC(q) = wL(q,K)
MC(q) = Cost of using L units of labor = wL
Suppose capital is fixed at K.
VC(q) = wL(q,K)
MC(q) = It takes 5 hours of prep time to prepare one more lecture, so MP of 1
hour of labor = 1/5
Wage = $10 per hour
MC of one more lecture = $10 / (1/5) = $ 50 V (q ) wL
AVC (q) =
=
q
q Suppose MPL is strictly decreasing in L (Diminishing Marginal Returns).
Then APL is strictly decreasing in L.
Then MC and AVC are strictly increasing in q, but AC may still decr. in q. Short Run:
Capital is fixed at K
MC(q) = w / MPL
AVC(q) = wL / q = w/APL Long Run
Capital and Labor are flexible
Develop concept of isocost line
Similar to budget line from consumer theory
Tangency of indiff curve and budget line = optimal for consumer
Tangency of isoquant and isocost line = optimal for producer In longrun, all costs are adjustable
Fixed cost of land: can sell off some land
Can fire managers / CEO
Can sell planes As before, firms have variety of input choices
Firm will determine optimal mix based on price of inputs Useful analytical tool: Isocost line
Specifies total cost of using combination of inputs
Similar to budget curve from consumer theory r is rental rate of capital
Even if firm owns capital, can think about implicit rental rate Slope of isocost curve =  w / r Slope of Isoquant = Slope of isocost line
But what do we need for an interior solution? q = L1/2K1/2, w = 4, r = 2 q = L + K, w = 4, r = 2 q = min{L,K}, w = 4, r = 2 MinL,K wL + rK subject to q = f(L,K)
Langrangian Approach MinL,K wL + rK subject to q = f(L,K)
Langrangian Approach MinL,K wL + rK subject to q = f(L,K)
Alternative Approach
MinK wL(q,K) + rK
FOC: Talked about minimizing cost given a fixed output
How about maximizing output given a cost? MaxL,K f(L,K) subject to wL + rK C MaxL,K f(L,K) subject to wL + rK C Suppose f(L,K) = (L2 + K2)1/2, w = 1, r = 2
Could look at tangency, but this will give exactly the
wrong answer. AC is Ushaped as one increases output
AC is downward sloping initially because AC is upward sloping eventually because
Hint: MC is going up because AC in longrun different from AC in shortrun
No fixed costs in longrun
Not diminishing marginal returns since both inputs can be
increased Action is from economies of scale
C(q) has economies of scale if AC(q) decreases as q increases
C(q) has no economies of scale if AC(q) is constant as q
increases
C(q) has diseconomies of scale if AC(q) increases as q increases Returns to Scale Economies of Scale Returns to scale is about production, economies of scale about costs
However, Returns to scale equivalent to economies of scale (book is
incorrect)
Increasing returns to scale
Economies of Scale
Constant returns to scale
No Economies of Scale
Decreasing returns to scale
Diseconomies of Scale Factors that drive scale effects Claim: If f(L,K) is CRS, then for all q,
C(q) = qC(1)
MC(q) = AC(q) = C(1) Pf: Argue by contradiction: suppose for some q’>1
1.
2. C(q’) > q’C(1): Will lead to contradiction when scaling up from 1 to q’
C(q’) < q’C(1): Will lead to contradiction when scaling down from q’ to 1 Practice makes perfect ...
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This note was uploaded on 11/30/2011 for the course ECON 311 taught by Professor Zambrano during the Fall '08 term at Cal Poly.
 Fall '08
 ZAMBRANO
 Microeconomics

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