Why is Anyone On Meal Plan?An Analysis of Dining Economics at Brown University By Zach, Grace, and Liv
Background • People need to eat • Many food options around Brown University • On campus options • Joes, Ratty, V-Dub, Blue Room, etc. • Off campus • Chipotle, Better Burger, Mama Kims, etc • Students have the option to eat at any of these establishments, but the method of payment differs between them
Many Ways to Pay • Off campus only accepts cash • On campus accepts Meal Credits (MC) or cash • Cost/meal is 1 swipe • Dollar value varies between institution • Joes - $6.60 • Ratty - $12.60, also dependent on time of day • “Although meals are available on a cash basis, plans offer a much lower per-meal cost and are therefore a better value.” – Food Services
Menu of Options Available Optimal : average cost/ meal if use up all the credits and points We convert points into credits 1 credit = 6.6 points
Survey • 117 Randomly Chosen Brown Students
Histogram of Survey Data # of participants # of meal credits used per week
Odd Observation • Most (~80%) of people are on meal plan • Most of those (72%) are on one of the two biggest plans • At the end of the year/semester, Joes is looted • 50% of people end the year with 20 or more unused meal credits • Average person wastes ~31.6 credits • Are people overpurchasing?
Questions • With a menu of meal plans available, and the option to not be on meal plan at all, how do people choose plans? • What does this choice say about peoples perception of off campus costs?
Standard Economic Explanation • People choose the plan that minimizes their total food costs • Buying larger plans that might waste credits is a product of peoples attempts to purchase larger bundles, get economies of scale. • People purchase on campus rather than off campus because it is cheaper
Simplifications/Assumptions in the Model • Sole determinant of behavior is desire to minimize costs • Quality, convenience, portion size, not considered • People’s consumption behavior stays the same no matter what plans they are on • People can only spend integer number of credits • People know their distribution of consumption • Once people run out of meals, they cannot eat at the on-campus eateries
Ideal VS Actual Data • Ideal data would be individual’s daily consumption pattern for a year, split into meal credits used, by eatery • Actual Data: We randomly sampled 94 people and asked how many meal credits they used yesterday and today and then derived their consumption pattern per week from there.
The Model Min j| i,zX ( i, j ,Z) Xi,j = Pj+Pr ( Ci>aj) * E [ ci-ai|ci> ai]*Z Ci~ D (μ , σ) • Plan j ＝aj ~ # of meals in the bundle Pj~ price of the bundle • Z – price per off-campus meal • X(I, j, z) – total cost of consumption • C i - # of total meals consumed per person • Pr( C i>aj) – probability of consuming more meals than the bundle • Flex 460 - Pr ( C i>546), Ci is annual consumption • Weekly 20 – Pr( Sum(Max( C i-3,0),1,224)>34) • E [ ci-ai|ci> ai] – expected # of meals consume off-campus
Methodology • Derive people’s meal credits consumption pattern by looking at their meal credits used in the past two days • Split into two groups and calculate its mean, distribution. • Big Eaters: People on the highest two meal plans, Flex 460 and 20 meals/week • Small eaters: Rest of the population • Calculate Probability consumption greater than max allowed, expected value given consumption is greater than max allowed, to determine expected meals beyond what is available on plan
Methodology • Given this number of meals, cost compare to being on no meals plan such that total cost = (mean consumption)*price Z • Implies cost that makes you indifferent between being on a given meal plan, or not, for a certain price of off campus food • The plan that has the lowest Z value is considered the cheapest
Answers to the Previous Question • Q: What are people’s perception of off campus costs? • Big eaters are consuming on campus meals at cost on average on par with the off campus meal. Small eaters are consuming at a rate that’s above average cost of off campus meals. • Q: With a menu of meal plans available, and the option to not be on meal plan at all, how do people choose plans? • Big eaters are cost conscious to a degree but they are not choosing the optimal plan. Small eaters are not cost minimizing.
New questions from the result • Why are big eaters on flex instead of weekly plans? • Why do small eaters choose to stay on meal plan?
Deferred Loss Realization • People may be sensitive to “wasting” meal credits • Odean gives account of traders who don’t sell losing investments quickly • People don’t like recognizing “losses” – even if they’ve already occurred • Credits are “wasted” when they are no longer able to be used • Flex gives less credits, so less are wasted, and only occurs at end of the year
Considering Wasted Meal Credits as a Cost • People may view meal credits as equivalent to money, don’t want to waste it • “Saving” when they waste fewer meal credits, even though fiscal cost already recognized • Thaler gives account of people who “save” in one account, while spending out of another “account” • Not using a credit has negative utility
Model Adjustment • Utility = Ideal consumption – Overconsumption – Under consumption • U = Ui - Pr ( Ci>aj) * E [ ci-ai|ci> ai]*Z - Pr ( Ci<aj) * E [ai-ci|ci<ai]*Z’ • Z’ is the “cost” of wasting a meal • Draw Graph to illustrate
Possible Reason for Small Eaters (-4400, 3900) (-4400, 3900) (-4200, 3900) (-4200, 3900) (-4000, 4000) (-4500, 4500) B=Behave, M=Misbehave
Principal-Agent Problem • Principal-agent relationship • Restaurant owner—waiter • Software company—salesman • Interests of agents are not perfectly aligned with those of the principals • Asymmetrical Information • Moral Hazard • OhadKadan, Philip J. Reny, and Jeroen M. Swinkels (2009) • Agent has no private information • Pure moral hazard • Agent’s only action is a participation decision
Survey • 117 Randomly Chosen Brown Students
Conclusion • Optimal plans for big eaters : 20 meals/ week small eaters: 14 meals/ week • Big Eaters are cost-conscious but appear to have some disutility with “wasting” meals. Hence they choose to switch to the flex even though the weekly plan is more cost minimizing. • Small eaters may be cost-conscious but the principal agent dilemma overrides their ability to minimize their cost.
References • Stefano DellaVigna, Ulrike Malmendier. 2005. “ Pay Not To Go To The Gym” • Kaniska Dam, David Perez-Castril. 2003. “ The Principal-Agent Matching Market” • Terrance Odean, 1998. “Are Investors Reluctant to Realize Their Losses?” • OhadKadan, Philip J. Reny, JeroenM. Swinkels. 2009. “ Existence of Optimal Mechanisms in Principal-Agent Problems” • "Meal Plan choices and Pricing." Brown Dining. N.p., Web. 1 Dec. 2012.