复旦大学：《产业经济学 Industrial Economics》教学课件_Industrial Organization 4 Markets for Differentiated Products

EFMD EQUIS CREDITED Industrial organization Lecture 4 Markets for Differentiated products 學火旦 于 udan university

Binglin Gong Fudan University Industrial Organization Lecture 4 Markets for Differentiated Products

Product Differentiation Most industries produce a large number of similar but not identical products Only a small subset of all possible varieties of differentiated products are actually produced. For example, most products are not available in all colors Most industries producing differentiated products are concentrated, in the sense that it is typical to have two to five firms in an industry Consumers purchase a small subset of the available product varieties

Product Differentiation • Most industries produce a large number of similar but not identical products. • Only a small subset of all possible varieties of differentiated products are actually produced. For example, most products are not available in all colors. • Most industries producing differentiated products are concentrated, in the sense that it is typical to have two to five firms in an industry. • Consumers purchase a small subset of the available product varieties

Two approches Product differentiation models are divided into two groups non-address models and address (location) models

Two approches Product differentiation models are divided into two groups: • non-address models, • and address (location) models

Diff product models Non-address approach Address Circular Linear Endogenous variety FⅨ ed variety Static Sequential static Sequential Cournot Bertrand Cournot Bertrand

Non Address approach Counot Competition Consider a two-firm industry producing two differentiated products indexed by i=1, 2. Following Dixit(1979)and Singh and Vives(1984), we assume the following (inverse) demand structure for the two products P1=a-Bq1-792 and p2=a-?91-Bq2, where A>0,8> (71) Implied assumptions There is a fixed number of two brands 2. Own-price effect dominates the cross-price effect: The price of a brand is more sensitive to a change in the quantity of this brand than to a change in the quantity of the competing brand

Non Address approach Counot Competition • Consider a two-firm industry producing two differentiated products indexed by i = 1, 2. Following Dixit (1979) and Singh and Vives(1984), we assume the following (inverse) demand structure for the two products: • Implied assumptions: 1. There is a fixed number of two brands. 2. Own-price effect dominates the cross-price effect: The price of a brand is more sensitive to a change in the quantity of this brand than to a change in the quantity of the competing brand

Going from Inverse demand Functions to Demand functions The demand structure exhibited in(7. 1)is formulated as a system of inverse demand functions where prices are functions of quantity purchased. In order to find the direct demand functions we need to invert the system given in(7.1) g1=a-bpi+cpa and 92=a+ ep1-bp2, where(7.2) a三 二,b= >0,c≡ >0

Going from Inverse Demand Functions to Demand Functions • The demand structure exhibited in (7.1) is formulated as a system of inverse demand functions where prices are functions of quantity purchased. In order to find the direct demand functions, we need to invert the system given in (7.1)

Degree of Brand differentiation The brands measure of differentiation, denoted by s IS 72 The brands are said to be highly differentiated if consumers find the products to be very different, so a change in the price of brand j will have a small or negligible effect on the demand for brand i Formally, brands are highly differentiated if 8 close to0. That is,when?2→0,( hence c→0)

Degree of Brand Differentiation • The brands' measure of differentiation, denoted by δ is 1. The brands are said to be highly differentiated if consumers find the products to be very different, so a change in the price of brand j will have a small or negligible effect on the demand for brand i. Formally, brands are highly differentiated if δ is close to 0. That is, when , (hence )

Degree of Brand differentiation The brands measure of differentiation, denoted by s IS 6≡ The brands are said to be almost homogeneous if the cross-price effect is close or equal to the own-price effect. In this case prices of all brands will have strong effects on the demand for each brand. more precisely, if an increase in the price brand j will increase the demand for brand i by the same magnitude as a decrease in the price of brand i, that is, when 8 is close to 1, or equivalently when r-B ( hence c→b

Degree of Brand Differentiation • The brands' measure of differentiation, denoted by δ is • The brands are said to be almost homogeneous if the cross-price effect is close or equal to the own-price effect. In this case, prices of all brands will have strong effects on the demand for each brand, more precisely, if an increase in the price brand j will increase the demand for brand i by the same magnitude as a decrease in the price of brand i, that is, when δ is close to 1, or equivalently when , (hence )

Cournot best response functions with product differentiation To simplify the exposition, we assume that production is costless, i.e., MC=0 Each firm i takes qj as given and chooses qi to maximize its profit maxT 1, 92)=(a-pqi-70q4 4,3=1, 2,i3.(7.3) The first-order conditions are given by 0=:4=a-2n-7g yielding best response functions given by a=R(q)=n″1j=1,2,i≠j (74)

Cournot Best Response Functions with Product Differentiation • To simplify the exposition, we assume that production is costless, i.e., MC=0. • Each firm i takes qj as given and chooses qi to maximize its profit: • The first-order conditions are given by yielding best response functions given by

Cournot Equilibrium with Product Differentiation Solving the best-response functions(7. 4) using symmetry, we have a,西十 q=2+T (26+ 7)21=1,2 (75) R2(q) R1()

Cournot Equilibrium with Product Differentiation • Solving the best-response functions (7.4), using symmetry, we have