Transcript economia.uniroma2.it

Microeconomics precourse – Part 3
Academic Year 2013-2014
Course Presentation
This course aims to prepare students for the Microeconomics
course of the MSc in BA. It provides the essential background in
microeconomics
PAOLO PAESANI
Office: Room B6, 3RD floor, Building B
Telephone: 06-72595701
E-mail: [email protected]
Office hours: to be agreed
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THEORY OF THE FIRM
Rational agents try to get as much as they can out of resources for a given
objective function and a set of constraints.
Rational firms operate to maximise profits given technological and market
constraints.
Main elements of the theory of the firm:
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Different views on the nature of firms
Technology
Profit maximisation in the short-run
Profit maximisation in the long-run
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THEORY OF THE FIRM
Individualistic firm: one individual working with tools and raw materials.
Classical theory of the firm: group of individuals with a specific
organisational structure and a set of property rights centred on the
owner / enterpreneur / employer. (centrally planned structure)
“An island of conscious power in an ocean of unconscious cooperation”.
Arguments supporting the classical theory of the firm: Coase (1937),
Alchian and Demsetz (1972).
Critiques of the classical theory of the firm
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THE CLASSICAL ENTERPRENEUR
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Enters into a contract with each of the individuals that supply productive services
to the firm which specifies the nature and duration of those services and the
remuneration for them;
Either takes a decision or has a right to insist that decisions are taken in his
interest, subject to his contractual obligations;
Has the right to the residual income from production, i.e. to the excess of
revenues over payments to suppliers of productive services;
Can transfer his rights in the residual income and his rights and obligations under
the contract to another individual;
Has the power to direct the activities of the suppliers of productive services,
subject to the terms and condition of their contracts;
Can change the membership of the producing group not only by terminating
contracts but also by entering into new contracts and adding to the group.
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CRITIQUES TO THE CLASSICAL THEORY OF THE FIRM
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Ownership structure (individual, concentrated, dispersed);
Control structure (composition of the board of directors, senior
executives);
Organization (large firms = complex hierarchical structures that implement
policy objectives into specific plans, monitor performance, transmit
information);
Information: acquisition, transmission to the points in the firm at which it
is required for decision making, evaluation;
Conflict of interest: individual within the same firms have different
objectives and plans based on which they formulate their decision,
possibility of a conflicts especially in case of asymmetric information;
INDUSTRIAL ORGANISATION + GAME THEORY.
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TECHNOLOGY AND PRODUCTION FUNCTION
Varian (1992)
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THE COBB-DOUGLAS PRODUCTION FUNCTION
Total utility : y(x1, x2)=(x1)a(x2)b a,b > 0
Total output produced combining two homogeneous inputs in a technologically
efficient way
Marginal product input 1: MPX1(x1, x2)= ∂U/∂x1= a(x1)a-1(x2)b
Additional output the firm obtains from marginally increasing its use of input 1
for a given quantity of input 2
Marginal utility input 2: MUX2(x1, x2)=b(x1)a(x2)b-1
Additional output the firm obtains from marginally increasing its use of input 2
for a given quantity of input 1
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MARGINAL RATE OF SUBSTITUTION
Varian (1992)
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TECHNOLOGY AND LONG-RUN PRODUCTION FUNCTION
Varian (1992)
We represent long-run production functions by means of isoquants
Combinations of inputs yielding the same output
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TECHNICAL RATE OF SUBSTITUTION
TRS
=
dx2/ dxX1
=
MPx1/MPx2
=
a(x1)a-1(x2)b/b(x1)a(x2)b-1
=
a(x2)/b(x1)
The technical rate of substitution
measures the slope of the isoquant
in absolute value
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SHORT-RUN PRODUCTION FUNCTION
y = f(x1, x2)
Where
y = total output
x1 = variable input (labour)
x2 = fixed input (capital)
While
dy/dx1 = f’(x1, x2) = MPx1
Is the marginal product of x1
(labour) = Additional amount of
output obtained employing an
additional quantity of x1 for a
givene quantity of x2.
Varian (2010)
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SHORT-RUN PRODUCTION FUNCTION
Points above the SRPF are not technologically feasible unless the amount of fixed
factor increases or technological progress occurs. Points below the SRPF are
feasible but technologically inefficient. A rational firm would not choose them.
If the SRPF is concave (as in the case shown above), the marginal product of x1 is
positive and diminishing . As x1 increases (for a given value of x2) total output
increases less than proportionally.
If the SRPF is a straight line sloping up, the marginal product of x1 is positive and
constant . As x1 increases (for a given value of x2) total output increases
proportionally.
If the SRPF is a convex, the marginal product of x1 is positive and increasing. As x1
increases (for a given value of x2) total output increases more than proportionally.
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FIXED AND VARIABLE FACTORS
Varian (1992)
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SHORT-RUN PROFIT MAXIMISATION
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SHORT-RUN PROFIT MAXIMISATION
Varian (2010)
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SHORT-RUN PROFIT MAXIMISATION
Varian (2010)
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PROFIT-MAXIMISATION IN THE LONG-RUN
In the long-run, the firm can choose the optimal level of both
inputs (no input is fixed). Determining the profit-maximising
input levels together with the optimal output level is done in
two stages:
Stage 1: Identification of the cost function.
Stage 2: determination of the optimal output level, based on
the cost function and on market demand.
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COST MINIMIZATION
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THE CONSUMER BEHAVIOUR
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D
A
Varian (2010)
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COST MINIMIZATION: MATHEMATICAL SOLUTION
Given the target level of output and input prices (firm is price taker), the
minimum cost input bundle is characterised by two conditions:
Tangency condition between the iso-cost line and the isoquant. The slope of
the budget line (equal to the ratio of the two input prices) is equal to the slope
of the isoquant equal to the technical rate of subsititutions
Technical feasibility condition: the optimal input combination belongs to the
isoquant corresponding to target output.
Translating these two condition under the assumption of a Cobb-Douglas
technology we obtain
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COST MINIMIZATION : MATHEMATICAL SOLUTION
1. a(x2)/b(x1) = (w1/w2)
2. y =(x1)a(x2)b
Solving the system composed by Equations 1 and 2 we obtain the firms’s input
demand functions conditional on target output and input prices
3. x1 =
4. x2 =
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COST MINIMIZATION : MATHEMATICAL SOLUTION
Substituting equation 3. and 4. in the generic cost function
C = w1 x1 + w2 x2 we obtain the following total cost function
=
Dividing total costs by the output level we obtain average costs
AC(y) = C(y)/y
Differentiating total costs by the output level we obtain marginal
costs, i.e. the cost of producing one additional unit of output
MC = dC(y)/dy
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COST CURVES
Varian (2010)
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COST CURVES
Varian (2010)
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PROFIT MAXIMIZATION IN THE CASE OF PERFECT COMPETITION
Varian (2010)
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PROFIT MAXIMIZATION IN THE CASE OF PERFECT COMPETITION
Varian (2010)
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PROFIT MAXIMIZATION IN THE CASE OF PERFECT COMPETITION
WHEN THE MARKET
PRICE IS EQUAL TO P1
PROFIT MAXIMISING
QUANTITY IS Q1. TOTAL
REVENUE IS EQUAL TO
(p1*q1), TOTAL COSTS
ARE QUALE TO (q1 *
Aac(q1)), TOTAL PROFITS
ARE QUAL TO TOT REV –
TOT COSTS.
P1
AC(q1)
q1
Varian (2010)
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REFERENCE
Varian H. (1992) Microeconomic Analysis, 3rd edition,
W. W. Norton & Company
Varian H. (2010) Intermediate Microeconomics, 8°
edition, W. W. Norton & Company
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