Allocation intimidates many students but it is really as simple as splitting the dinner check.
We have all gone to a restaurant for dinner with several others. We are having a great time, but eventually the check comes to the table and we are faced with the costing problem of deciding how to split the bill. Remember the three methods of distribution: guessing, direct costing, and allocation.
Split the Check By Guessing
This is done often. It works by each person guessing at their share and usually doesn’t work very well. People tend to underestimate their cost. They can forget what they ordered: particularly if alcohol is consumed too! They may think only of the menu price and not of the added taxes and tip.
The typical result is that the last person left with the check and some cash is stuck with making up the difference out of his or her own pocket. If you are in this costing situation and guessing is the costing choice my advice is to quickly put down some money and leave as soon as possible!
Split the Check By Allocation
Another costing choice is just to split the check “evenly.” If the total bill came to $160 with four eaters we would see each cost of $40. This is simply an allocation process and we have all done it.
The cost pool is $160. It is an aggregation of all the items ordered. Cost is then allocated on the basis of number of eaters. This can be thought of as either a rate method or proportion method. Both yield the same results.
The rate method divides the cost pool ($160) by number of eater (4) and calculates the rate as $40/eater.
If each eater is paying their own bill we have:
1 eater X $40/eater = $40
If someone is paying for another we would have:
2 eaters X $40/eater = $80
The proportion method looks at the how the base is distributed. It divides the each of the eaters (1) by the total number of eaters (4) and calculates that each eater is 25% of the total.
If each eater is paying their own bill we have:
25% X $160 = $40
If someone is paying for another we would have their proportion as 50% and:
50% X $160 = $80
Split the Check By Direct Costing
Direct costing either requires asking for separate checks or meticulously going through the check and trying to establish each eater’s consumption. This can certainly be done, but it takes time and some math.
The extra effort explains why restaurants prefer a single bill per table so they avoid the time (and cost) of the extra effort required for separate checks. It also explains why we tend to prefer allocating the check.
Behavioral Considerations
Perhaps you went to this meal not hungry or on a diet and only ordered a small salad. How do you feel paying the same amount as the eater with the lobster, desert, and three drinks? The allocation simply does not reflect your consumption and you are being over charged.
The technical term for this effect is cross subsidization. You are subsidizing someone else’s great meal.
You could also think of the motivation for consumption. When the check is going to be allocated you know that every $10 extra you order would only cost you $2.50. (You will only pay the 25% proportion of the incremental $10.) Maybe this is another reason the restaurants prefer the single check!
If you know the check is going to be allocated my advice is to forget the diet. Have a great meal and order an extra lobster to take home!
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