Liquor Store Math Revisited

A few months ago, I used basic mathematics to answer an important question: Is it worth driving to Superior from Duluth to take advantage of lower sales taxes and save money on off-sale alcohol purchases?

My answer, based on a sample story problem, was that Duluthians only save money shopping in Superior if they buy a lot of booze -- like $45 or more, at least.

Since that column ran, a number of people have suggested I publish an official equation for this problem, so they can simply plug in the appropriate numbers for their circumstances.

Normally I don't take requests, but this is an important subject for which I feel obligated to share my knowledge. The equations below will allow any Duluthian capable of passing high school algebra to calculate the real cost of choosing a neighborhood liquor store vs. crossing a bridge to Superior.

MN equation -- [r + r (0.10375)] + [d (0.24)] + [x (t/60)] = c
WI equation -- [r + r (0.055)] + [d (0.24)] + [x (t/60)] = c

r = retail price of liquor purchase

0.10375 = sum of Minnesota sales tax, Minnesota alcohol sales tax and Duluth sales tax

0.055 = sum of Wisconsin sales tax and Douglas County sales tax

d = roundtrip distance in miles between your house and the liquor store

0.24 = IRS standard deduction rate for miles driven for "medical" purposes

x = hourly compensation for time spent driving (It's up to you to decide what your time is worth, but for reference Minnesota's minimum wage is $6.15.)

t = minutes it takes to make the roundtrip

60 = total minutes in an hour

c = actual total cost of your purchase

Certain variables, of course, cannot be included in an equation but should be considered with the equation results. For example, the economic concept of "opportunity cost," factors in things such as the attractiveness of cashiers. The importance of such things varies from person to person, but the potential effect on the bottom line should also be noted. A person could save a significant amount of money by either obtaining a discount through a relationship with a liquor store cashier, or lose even more money by marrying and divorcing one. Such things are difficult to predict.

Paul Lundgren is a newspaper columnist and a very nice man. His e-mail address is mail @ paullundgren.com.