IO 2015 Menu Pricing _ lecture notes

MENU PRICING

Industrial Organiza/on 51

Spo/fy


Ipad


Menu pricing

•  Goods are offered in different versions at different prices – Hardcover/soAcover book – Apps/SoAware •  Basic (with ads)/Premium

– Movies •  3D/2D; Theatre/DVD/TV;

– First/business/economy classes in air transport •  Menu pricing is a tool for second degree price discrimina/on


Monopoly menu pricing

•  Define a consumer’s u/lity as = U(θ,s)-‐p if he buys a good of quality s at

price p = 0 if he does not buy

•  Consumers are heterogeneous with respect to their taste for quality: – High valua/on consumers: θ=θ2 – Low valua/on consumers: θ=θ1 , θ1<θ2

– Propor/on λ of high valua/on consumers in the popula/on



•  A monopolist produce two quali/es of the good – High quality s2 at cost c2 – Low quality s1 at cost c1

•  The high quality is not less costly to deliver: c1≤c2



•  Assump/ons 1.  For s=s1, s2, U(θ2,s)>U(θ1,s) Consumers with a high taste for quality parameter are ready to pay more for quality s 2. U(θ2,s2)-‐U(θ2,s1)>U(θ1,s2)-‐U(θ1,s1) Consumers with a high taste for quality parameter are ready to pay more for quality at the margin 3. U(θ1,si)>ci


Single quality

•  If the monopolist sells a single quality, he has 4 different op/ons:

1.  Quality s1 at price p=U(θ1, s1) giving a profit π=U(θ1, s1)-‐c1

2.  Quality s1 at price p=U(θ2, s1) giving a profit π=λ[U(θ2, s1)-‐c1]

3.  Quality s2 at price p=U(θ1, s2) giving a profit π=U(θ1, s2)-‐c2

4.  Quality s2 at price p=U(θ2, s2) giving a profit π=λ[U(θ2, s2)-‐c2]


Single quality

•  Assume that U(θ1, s2)-‐U(θ1, s1)≥c2-‐c1

•  In this case, the monopolist offers quality s2 either at price U(θ1, s2) or at price U(θ2, s2)

•  The second op/on is preferred if the propor/on of high valua/on consumers is high enough:


λ ≥U(θ1, s2 )− c2U(θ2, s2 )− c2

= λ0

Two quality levels

•  Suppose that the monopolist offers the two quali/es s1 and s2 at prices p1 and p2

•  Consumers with a high valua/on will buy the quality s2 at price p2 if:

U(θ2, s2)-‐p2 ≥ 0 U(θ2, s2)-‐p2 ≥ U(θ2, s1)-‐p1

•  Consumers with a low valua/on will buy the quality s1 at price p1 if:

U(θ1, s1)-‐p1 ≥ 0 U(θ1, s1)-‐p1 ≥ U(θ1, s2)-‐p2


Two quality levels

•  Op/mal prices are – p1=U(θ1, s1) – p2=U(θ2, s2)-‐[U(θ2, s1)-‐U(θ1, s1)]

•  When the monopolist supplies two quali/es, the high quality is offered at a discount: p2<U(θ2, s2) for incen/ve reasons

•  The profit is equal to λ[U(θ2, s2)-‐[U(θ2, s1)-‐U(θ1, s1)]-‐c2]+(1-‐λ)[U(θ1, s1)-‐c1]


Comparison

•  Suppose λ>λ0 •  If the firm sells the high quality s2 at price U(θ2, s2), the profit is λ[U(θ2, s2)-‐c2]

•  Menu pricing increases the profit if (1-‐λ)[U(θ1, s1)-‐c1] ≥ λ[U(θ2, s1)-‐U(θ1, s1)]

•  This condi/on is sa/sfied if λ<λ* and there exists parameters value for which λ0<λ<λ*


Market expansion Cannibaliza/on

Quality choice

•  Suppose that quali/es are variable and denote by c(s) the cost of producing a good of quality s •  Assume that c’>0 and c’’>0 •  With menu pricing the profit is equal to λ[U(θ2, s2)-‐[U(θ2, s1)-‐U(θ1, s1)]-‐c(s2)]+(1-‐λ)[U(θ1, s1)-‐c(s1)]

•  The op/mal quali/es maximize this expression •  Finally assume that dU(θ,s)/ds>0


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IO 2015 Menu Pricing _ lecture notes