Bundling and Matching

Scenario: Points A$,$ B$,$ C$,$ and D in the Cartesian system below represent four buyers' willingness to pay for goods $1$ and $2($ r $1$ and r $2,$ respectively$).$ The seller's cost of producing Goods $1$ and $2$ are $c1=0$ and $c2=0,$ respectively.

FIGURE $1$: Consumers' preferences for Goods $1$ and $2$

Organize the information shown in Figure $1$ concerning the buyers' willingness to pay for Goods $1$ and $2($ r $1$ and r $2,$ respectively$)$ in the table below. $(2$ points$)$

TABLE $1$

$\backslash$table$[[$Buyer$,$r$1,$r$2],[$A$,,],[$B$,,],[$C$,,],[$D$,,]]$

Using the information in Table $1$ and Figure $1,$ determine the consumption choices of each buyer if the seller adopts a Pure Components strategy, setting the price of Good $1$ at $p1=80$ and the price of Good $2$ at $p2=80.$ Show your work. $(4$ points$)$

Using the information in Table $1$ and Figure $1,$ determine the consumption choices of each buyer if the seller adopts a Pure Bundling strategy, setting the price of the bundle at $pb=100.$ Show your work. $(4$ points$)$

Using the information in Table $1$ and Figure $1,$ determine the consumption choices of each buyer if the seller adopts a Mixed Bundling strategy, setting the price of Good $1$ at $p1=90,$ the price of Good $2$ at $p2=90,$ and the price of the bundle at $pb=120.$ Show your work. $(4$ points$)$

Using the information in Table $1$ and Figure $1,$ determine the consumption choices of each buyer if the seller adopts a Mixed Bundling strategy, setting the price of Good $1$ at $p1=90,$ the price of Good $2$ at $p2=90,$ and the price of the bundle at $pb=120.$ Show your work. $(4$ points$)$

Using your answer to question $2,$ calculate the profit obtained by the seller who adopts a Pure Components strategy, setting the price of Good $1$ at p$1=80$ and the price of Good $2$ at p$2=80.$ Show your work. $(4$ points$)$

Using your answer to question $3,$ calculate the profit obtained by the seller who adopts a Pure Bundling strategy, setting the price of the bundle at $pb=100.$ Show your work. $(4$ points$)$

Using your answer to question $4,$ calculate the profit obtained by the seller who adopts a Mixed Bundling strategy, setting the price of Good $1$ at $p1=90,$ the price of Good $2$ at $p2=90,$ and the price of the bundle at $pb=120.$ Show your work. $(4$ points$)$

Using the information in Table $1$ and your answers to questions $1$ to $7,$ indicate the strategy that generates the highest profit level for the seller. Mark one option. $(2$ points$)$

A$)$ Pure Components

B$)$ Pure Bundling

C$)$ Mixed Bundling