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# Suppose Sydney’s healthy days are produced by H (health stock) with a production function of Healthy days

INSTRUCTIONS TO CANDIDATES

1. (13 points) Suppose Sydney’s healthy days are produced by H (health stock) with a production function of Healthy days = 25 + 10H - H2

in the increasing region of the function. Suppose that raising the health stock by one unit requires the following resources:

Food at a cost of \$100

Four doctor checkups at a cost of \$30 each, where he misses half a day o↵ of work for each

Five workouts at a cost of \$40 each, where he does not miss any work

Suppose the real interest rate is 6%, and his depreciation rate is 4%.

Professor Ngo hires Sydney as a tutor to help her understand the world of anime. She wants to incentive him to take care of himself. Specifically, she wants Sydney to achieve an optimal health stock of 4 units. Calculate the wage she should pay Sydney.

2. (18 points) In response to Professor Noel’s excessive comments on their group presentation, Theo, Bia, and Tye decide to switch the topic for their group paper. They propose to implement a policy that grants U.S. citizenship to undocumented immigrants. They will use undocumented immigrants as their treated group and Latinx U.S. citizens as their control group. They plan to implement the policy in 2025, using 2022 as their before time period and 2040 as their after time period. They plan to estimate the e↵ect of their program using the standard di↵erence-in-di↵erences regression below,

and they choose life expectancy at birth as their outcome.

Life Expectancyit = ;30 + ;31Treatmenti + ;32Postt + ;33Treatment Postit + ✏it

(a) (7 points) Provide a reasonable prediction for the value and sign of ;32, and explain (2 sentences max). You should provide a specific number.

(b) (11 points) Do we expect ;33 to be large and positive, small and positive, zero, small and negative, or large and negative? Explain using the relevant theories on socioeconomic disparities in health (5 sentences max).

3. (8 points) Name one factor that is an important contributor to socioeconomic disparities in health that is not currently included in any of the theories discussed in class. (We discussed discrimination in class, so you should name something di↵erent.) Briefly explain why you think it causes socioeconomic disparities in health.

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