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 1

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 2

Micro 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 3

Micro • • • • • • 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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Micro • • • • • • 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. 5

Micro TECHNOLOGY AND PRODUCTION FUNCTION Varian (1992) 6

Micro THE COBB-DOUGLAS PRODUCTION FUNCTION Total utility : y(x 1 , x 2 )=(x 1 ) a (x 2 ) b a,b > 0 Total output produced combining two homogeneous inputs in a technologically efficient way Marginal product input 1: MPX 1 (x 1 , x 2 )= ∂U/∂x 1 = a(x 1 ) a-1 (x 2 ) 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: MUX 2 (x 1 , x 2 )=b(x 1 ) a (x 2 ) b-1 Additional output the firm obtains from marginally increasing its use of input 2 for a given quantity of input 1 7

Micro MARGINAL RATE OF SUBSTITUTION Varian (1992) 8

Micro 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 9

Micro TECHNICAL RATE OF SUBSTITUTION TRS = dx 2 / dxX 1 = MPx 1 /MPx 2 = a(x 1 ) a-1 (x 2 ) b /b(x 1 ) a (x 2 ) b-1 = a(x 2 )/b(x 1 ) The technical rate of substitution measures the slope of the isoquant in absolute value 10

Micro SHORT-RUN PRODUCTION FUNCTION y = f(x 1 , x

2

) Where y = total output x 1 = variable input (labour) x 2 = fixed input (capital) While dy/dx 1 = f’(x 1 , x

2

) = MPx 1 Is the marginal product of x 1 (labour) = Additional amount of output obtained employing an additional quantity of x 1 for a givene quantity of x 2 .

Varian (2010) 11

Micro 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 x 1 positive and diminishing . As x 1 increases (for a given value of x 2 ) total output increases less than proportionally.

is If the SRPF is a straight line sloping up, the marginal product of x 1 constant . As x 1 increases (for a given value of x 2 is positive and ) total output increases proportionally.

If the SRPF is a convex, the marginal product of x 1 is positive and increasing. As x 1 increases (for a given value of x 2 ) total output increases more than proportionally.

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Micro FIXED AND VARIABLE FACTORS Varian (1992) 13

Micro SHORT-RUN PROFIT MAXIMISATION 14

Micro SHORT-RUN PROFIT MAXIMISATION Varian (2010) 15

Micro SHORT-RUN PROFIT MAXIMISATION Varian (2010) 16

Micro 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. 17

Micro COST MINIMIZATION 18

Mic ro THE CONSUMER BEHAVIOUR E A D Varian (2010) 19

Micro 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 20

Micro COST MINIMIZATION : MATHEMATICAL SOLUTION 1. a(x 2 )/b(x 1 ) = (w 1 /w 2 ) 2. y =(x 1 ) a (x 2 ) 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. x 1 = 4. x 2 = 21

Micro COST MINIMIZATION : MATHEMATICAL SOLUTION Substituting equation 3. and 4. in the generic cost function C = w 1 x 1 + w 2 x 2 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 22

Micro COST CURVES Varian (2010) 23

Micro COST CURVES Varian (2010) 24

Micro PROFIT MAXIMIZATION IN THE CASE OF PERFECT COMPETITION Varian (2010) 25

Micro PROFIT MAXIMIZATION IN THE CASE OF PERFECT COMPETITION Varian (2010) 26

Micro PROFIT MAXIMIZATION IN THE CASE OF PERFECT COMPETITION P1 AC(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.

q1 Varian (2010) 27

Micro 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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