$8.$ Individual Problems $14-6$

$At$ a student caf$,$ there are equal numbers $of$ two types $of$ customers with the following values. The caf$$ owner cannot distinguish between the two types $of$ students because many students without early classes arrive early anyway $(i.e.,$ she cannot price$-$discriminate$).$

Students with Early Classes

Students without Early Classes

Coffee $7363$

Banana $55105$

The marginal cost $of$ coffee $is10$ and the marginal cost $of$ a banana $is40.$

The caf$$ owner $is$ considering three pricing strategies:

$1.$ Mixed bundling: Price bundle $of$ coffee and a banana for $168,or$ just a coffee for $73.$

$2.$ Price separately: Offer coffee $at63,$ price a banana $at105.$

$3.$ Bundle only: Coffee and a banana for $128.Do$ not offer goods separately.

Assume that $if$ the price $ofan$ item $or$ bundle $isno$ more than exactly equal $to$ a student's willingness $to$ pay, then the student will purchase the item $or$ bundle.

For simplicity, assume there $is$ just one student with $an$ early class, and one student without $an$ early class.

Price Strategy

Revenue from Pricing Strategy

Cost from Pricing Strategy

Profit from Pricing Strategy

$1.$ Mixed Bundling

$2.$ Price Separately

$3.$ Bundle Only

Pricing strategy yields the highest profit for the caf$$ owner.