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

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PAOLO PAESANI Office: Room B6, 3RD floor, Building B Telephone: 06-72595701 E-mail: paolo.paesani@uniroma2.it Office hours: to be agreed

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:

• 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

• 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

• 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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Varian (1992)

TECHNOLOGY AND PRODUCTION FUNCTION

Micro

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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

Micro

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Varian (1992)

MARGINAL RATE OF SUBSTITUTION

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Varian (1992)

TECHNOLOGY AND LONG-RUN PRODUCTION FUNCTION

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

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.

11 Varian (2010)

SHORT-RUN PRODUCTION FUNCTION

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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.

13 Varian (1992)

FIXED AND VARIABLE FACTORS

Micro

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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)

Micro

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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

A

D

E

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

Varian (2010)

P1

q1

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.

AC(q1)

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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