Why is Anyone On Meal Plan? An Analysis of Dining Economics at - PowerPoint Presentation

Why is Anyone On Meal Plan? An Analysis of Dining Economics at Brown University By Zach, Grace, and Liv

Background People need to eatMany food options around Brown University On campus optionsJoes, Ratty, V-Dub, Blue Room, etc.Off campusChipotle, Better Burger, Mama Kims, etcStudents have the option to eat at any of these establishments, but the method of payment differs between them

Many Ways to PayOff campus only accepts cash On campus accepts Meal Credits (MC) or cashCost/meal is 1 swipeDollar value varies between institutionJoes - $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 Plan Cost Meals/WeekMeals/YearOptimal Cost/Meal% on plan Flex 460$4,284 N/A546$7.8550.0%Flex 330$4,030 N/A361$11.167.5%Flex 240$3,654 N/A 261 $14.00 10.0% Meals/Week 20 $4,284 20 34$6.3621.5%Meals/Week 14$4,030 1427$8.480.9%Meals/Week 10$3,654 1019$10.781.9% 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 meal credits used per week # of participants

Odd ObservationMost (~80%) of people are on meal plan Most of those (72%) are on one of the two biggest plansAt the end of the year/semester, Joes is looted50% of people end the year with 20 or more unused meal creditsAverage 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 ExplanationPeople 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 costsQuality, convenience, portion size, not consideredPeople’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 consumptionOnce 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,z X ( i, j ,Z) Xi,j = P j +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 bundleZ – price per off-campus mealX(I, j, z) – total cost of consumptionC i - # of total meals consumed per person Pr ( C i>aj) – probability of consuming more meals than the bundleFlex 460 - Pr ( C i>546), Ci is annual consumptionWeekly 20 – Pr( Sum(Max( C i -3,0),1,224)>34) E [ c i -a i|ci> ai ] – expected # of meals consume off-campus

MethodologyDerive 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/weekSmall 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 ZImplies cost that makes you indifferent between being on a given meal plan, or not, for a certain price of off campus foodThe plan that has the lowest Z value is considered the cheapest

Results (1) Distribution Big Eaters Flex 460 Purchasers (subset of Big Eaters)Little Eatersn 735721Avg. meals/year567.67535.36378.67Std. Dev31.1935.3941.28Pr exceed daily limit ( 20, 20, 14) 8.30% 10% 9.10% Pr exceed weekly limit (20, 20, 14)18%11%14.30%Pr exceed annual limit(Flex 460, Flex 460, Flex 330)84%39.00%66%Annual expected meals over max (20, 20, 14)4.22 4.518 27.2 Annual expected meals over max ( Flex 460, Flex 460, Flex 330) 29.2 10.14 26.598

Results (2) Distribution Big Eaters Flex 460 Purchasers (subset of Big Eaters)Little EatersBreakeven$7.61 $8.03$11.48Optimal Meal Plan20/week20/week14/weekSavings vs. 2nd best, Z=10$247.82 $86.04 ($506.70)

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 creditsOdean gives account of traders who don’t sell losing investments quicklyPeople don’t like recognizing “losses” – even if they’ve already occurred Credits are “wasted” when they are no longer able to be usedFlex 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 recognizedThaler gives account of people who “save” in one account, while spending out of another “account” Not using a credit has negative utility

Model AdjustmentUtility = Ideal consumption – Overconsumption – Under consumption U = Ui - Pr ( Ci >aj) * E [ ci-a i|ci> ai ]*Z - Pr ( Ci<aj) * E [ai-c i|ci< ai ]*Z’Z’ is the “cost” of wasting a mealDraw Graph to illustrate

Big Eater Explanation Weekly 20 Flex Pr Wasting Meal/Day 57%N/A Pr Wasting Meal/YearN/A75%Expected "Wasted" Meals16817Dollar Cost$4,299.36$4,385.40Disutiliy Coeff (Z’) 0.57 0.57 New Utility 4395.12 4395.09

Possible Reason for Small Eaters B=Behave, M=Misbehave (-4400, 3900) (-4400, 3900)(-4200, 3900) (-4200, 3900)(-4000, 4000)(-4500, 4500)

Principal-Agent Problem Principal-agent relationshipRestaurant owner—waiterSoftware company—salesmanI nterests of agents are not perfectly aligned with those of the principals Asymmetrical Information Moral HazardOhad Kadan, Philip J. Reny, and Jeroen M. Swinkels (2009) Agent has no private informationPure 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/ weekBig 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.

ReferencesStefano 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?” Ohad Kadan, Philip J. Reny, Jeroen M. Swinkels. 2009. “ Existence of Optimal Mechanisms in Principal-Agent Problems”"Meal Plan choices and Pricing." Brown Dining. N.p., Web. 1 Dec. 2012.