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