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Of course, if the regular customer comes in more frequently because of Groupon, it still is \$77.50 the restaurant gains for each extra time that customer comes in. Your analysis assumes the regular customer comes in with the same frequency with or without the discount.

Does the restaurant keep the original \$7.50 regardless of whether the Groupon is redeemed or not? If so, this income should be taken into account as well. (For those that are not redeemed (new or regular customers), the restaurant is getting \$7.50 and providing \$0 of food/service.)

The question is how likely are regular customers to obtain a coupon. At the time the coupons are offered only a small proportion of the people offered to will be regular customers. Even if they have a higher take-up rate it is likely there numbers will be smaller than new customers. My understanding (I'm in Australia so I can't try it out) is that it is only one coupon per customer.

I'm reminded of the "toy" problems in calculus classes: If Giorgio's offers a coupon worth x dollars, it's profit changes by f(x). Find the value of x that maximizes the profit." As you correctly point out, if a meal at Giorgio's costs \$30, then a \$30 coupon is foolish (unless used as a "loss leader").

I think the conclusion is that the businesses that use Groupon need to be smart about how they use it. A well-designed statistical experiment wouldn't hurt: try offering several coupons, measure the results, and use statistics to find an optimal value. In fact, this seems like a valuable extra service that Groupon could offer it's customers...for a fee, of course.

I've seen Groupon deals or other similar ventures that require the individual to be a "new customer" to redeem the coupon. That type of stipulation would help safeguard the business, although I have no idea of how many businesses actually make this rule.

Even this is optimistic, no? Is the provision of the meal free to the restaurant? Can the marginal customer really so immensely profitable?

The restaurant preps and serves the regular diners regardless, so the Groupon costs the restaurant \$22.50 for each regular regardless.

New diners spending \$100 generates \$77.50 in revenue. Suppose that the \$100 meal costs the restaurant as little as \$50, implying \$22.50 in profit for each new customer. Then breaking even requires one new customer for each regular.

Diners spending \$30 generates \$7.50 in revenue, which assuming the same 100% mark-up of \$15, implies a \$7.50 loss of profit. In this case, the restaurant loses money on every customer.

If diners spend \$30, the restaurant must spend less than \$7.50 on the actual provision of food in order to break even just on the new customers. That implies that if the restaurant is marking up costs only 200% on those \$30 meals then it still loses money no matter how many new customers show up.

The restaurant presumably expects to profit from the Groupon by generating new regulars who then pay back the restaurant in the long run.

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