Problem Set 1 Solutions Upload

Problem Set #1: Answers Q1a: [5 points] Utility for  Steak and Eggs is 13 [ BEST Option!]  Kale Salad is -1.5  Cookies is 10 Q1b: [5 points] A miracle pill is discovered that halves the negative health impact of cookies. How does this impact your diner’s choice? Solution: Utility for  Steak and Eggs is 13  Kale Salad is -1.5  Cookies is 15 [ BEST Option!] Q1c: [5 points] What effect does the miracle pill have on the diner’s health H? Interpret this result. Does this mean the diner would be better off without the miracle pill? Solution: the consumer chooses the least healthy option and achieves a lower health level than under b (-5 versus -1) despite the fact that the pill intends to promote health. The utility is still higher than under a [15 versus 13] so the consumer is better off. Q1d: [optional not graded and no points] Solution: One intuitive way to approach this problem is to calculate the life-time consequence of a meal choice in period 0. Suppose the consumer chooses Steaks and eggs in t=0, then the life time utility payoffs can be summarized in the table below: t 2*Z_t ½*H_t U_t 0 14 -1 13 1 0 -1 -1 2 0 -1 -1 . 0 -1 -1 . 0 -1 -1

The key observation is that leisure only enters in period 0, whereas the health part matters for every period thereafter as well. Lifetime utility of a meal choice in t=0 is then given by: 𝑈 0 = 2𝑍 0 + 1 2 ∗ ∑ 𝛿 𝑡 𝐻 0 ∞ 𝑡=0 = 2𝑍 0 + 1 2 ∗ 1 1 − 𝛿 H 0 For 𝜹 = ?. ?? we have ? ? = ?𝒁 ? + ?𝑯 ? : Utility for  Steak and Eggs is 10 [ BEST Option!]  Kale Salad is 6  Cookies is -20 For 𝜹 = ?. 𝟗 we have ? ? = ?𝒁 ? + ?𝑯 ? Utility for  Steak and Eggs is 4  Kale Salad is 21 [ BEST Option!]  Cookies is -80 So as 𝜹 becomes sufficiently large, consumers go for the “healthiest” food option. Question 2: Grossman Model Qa: [25 points] Solution: A first observation is that time productive, T_p=24-T_s. Filling in the third equation from above we have T_p=24-T_s=24-( ?? − 𝑯) =H. Furthermore, we have T_p=T_H+T_z. Together we can rewrite the first equation as 𝑯 = ? 𝒑 = ? 𝑯 + ? 𝒁 = ? ∗ √? 𝑯 + ? − ? Solving for T_Z we have the PPF ? 𝒁 = ? ∗ √? 𝑯 + ? − ? − ? 𝑯 Point A is now T_H=T_Z=0. Point E=T_H=24 and T_Z=0. To find C, we search for the maximum of T_Z. We construct the first derivative of the PPF with respect to T_H and set this to zero. This yields 𝒅? 𝒁 𝒅? 𝑯 = ? √? 𝑯 + ? − ? = ? Solving for T_H we have T_H=8 and T_Z=4. The figure below shows this graphically:

Question 3: ### Stata code [35 points] ******************************************************************************** **** Analysis Files ******************************************************************************** . *** load data . . use nsch_2022_topical.dta, clear . . *insheet using nsch_2022_topical.csv, clear . . *** Question a construct obesity . . tab bmiclass Body Mass Index, Percentile | Freq. Percent Cum. ----------------------------------------+----------------------------------- Less than the 5th percentile | 2,831 8.61 8.61 5th percentile to less than the 85th pe | 20,293 61.68 70.29 85th percentile to less than the 95th p | 4,783 14.54 84.83 Equal to or greater than the 95th perce | 4,992 15.17 100.00 ----------------------------------------+----------------------------------- Total | 32,899 100.00

. . gen obese=bmiclass==4 . . *** keep children 10-17 . . keep if sc_age_years>9 & sc_age_years!=. (29,930 observations deleted) . . *** drop missing BMI class . . drop if bmiclass==. (0 observations deleted) . . **** Question b . sum obese [aw=fwc] Variable | Obs Weight Mean Std. Dev. Min Max -------------+----------------------------------------------------------------- obese | 24,173 34645314.7 .1594208 .3660756 0 1 . . *** About 15.9 percent of children aged 10-17 are obese . . *** Question c . . table higrade [aw=fwc], c(mean obese) ------------------------------------------------------ Highest Level of Education among | Reported Adults | mean(obese) -----------------------------------------+------------ Less than high school | .172207 High school (including vocational, trade | .2428011 More than high school | .1342235 ------------------------------------------------------ . . *** Only 13.4 percent of children are obese if their parents highest level of ed > ucation exceeds high school, compared to 24.3% and 17.2% if parents completed hi > gh school or less. This suggests that parental education is a predictor of child > hood obesity . . gen belowFPL=fpl_i1<=100

9 hours | .1359181 10 hours | .1354365 11 or more hours | .2122839 No valid response | .0712427 ------------------------------- . . *** There appears to be a u-shaped relationship between hours slept and obesity. > oebsity rates fall from 22.5% as children sleep less than 6 hours to 13.5% for > kids who sleep 10 hours, but then obesity rates increase again to 21.2% for kids > who sleep more than 11 hours . . table physactiv [aw=fwc], c(mean obese) ------------------------------- Exercise, Play | Sport, or | Physical Activity | for 60 Minutes | mean(obese) ------------------+------------ 0 days | .2193081 1 - 3 days | .1799864 4 - 6 days | .1211642 Every day | .1185496 No valid response | .1226597 ------------------------------- . . *** Physical activity os strongly negatively correlated with obesity. Only 11.8% > of children who are exercising 60 minutes every day are obese compared to 21.9% > who don't exercise for 60 minutes . ############ (incomplete) R code ########################## ## Choose Directory rm(list = ls()) setwd("C:/Users/Martin Hackmann/Documents/GitHub/Teaching/Econ131/Problem Set/PS1") ### Load dataset and save as "data" data=read.csv("nsch_2022_topical.csv") ### Question a construct obesity indicator

### tabulate data$bmiclass variable table(data$bmiclass) ### Contruct indicator data$obese=data$bmiclass=="Equal to or greater than the 95th percentile" #### identify folks 9 years and older and whose age is non-missing ind=data$sc_age_years>9 & is.na(data$sc_age_years)=="FALSE" ### only keep sample rows for which that is true data=data[ind,] ### Question b (use weighed mean from stats package) weighted.mean(data$obese,data$fwc) ### Question c ### Education ### Loop through unique realizations of education variable ### For each realization, display realization, identify correpsonding rows in the data, and present the weighted mean for (value in unique(data$higrade)) { print(value) ind=data$higrade==value print(paste("Share obese= ",weighted.mean(data$obese[ind],data$fwc[ind]))) } ### screentime table(data$screentime) for (value in unique(data$screentime)) { print(value)