Aqueous hydrochloric acid reacts with magnesium to produce hydrogen gas according to the balanced equation below. 2 HCl(aq) + Mg(s) → MgCl 2(aq) + H 2(g) If 250.0 mL of 3.00 M HCl is combined with 9.92 g Mg, what volume of hydrogen gas can be produced? Assume the temperature and pressure of the gas are 25 °C and 0.988 atm, respectively. ( R = 0.08206 L ⋅atm/mol ⋅K)

A balloon has a volume of 2.37 liters at 24.0°C. The balloon is heated to 48.0°C. Calculate the new volume of the balloon.

Externalities Question 1 Consider a group of friends who switch from driving to work to taking the bus. This makes the bus crowded, annoying the existing passengers. 

Readings (a) What is the empirical strategy of Green et al. (2016)? Is it just a difference-in-difference or something else? What is the treatment group? What is the control group? What is the synthetic control approach? (b) Describe the three empirical strategies used in Asquith et al. (2023). (c) Discuss potential costs and benefits that should be considered in a cost-benefit analysis of a tax on sugary beverages. What is the question that Colchero et al. (2017) ask, and what do they find?

Math-Based Problems Write your answers to the following math-based problems on a sheet (or sheets) of paper. Make sure to show all your work and clearly label your answers. You will upload an image or PDF scan of your work. 

Linear Regression Question 1 Consider the following regression equation: 

Retrospective reimbursement is:

In 1983, in an attempt to control costs, Medicare introduced the Prospective Payment System (PPS). In the first few years after its introduction, costs grew slowly. However, after 1988, cost increases crept back up. Which of the following is not a reason for the resurgence in cost growth after 1988?

School Competition One strategy for improving K-12 education is for government to provide families with vouchers that they can use to pay for any school (public or private) of their choosing. The hope is that competition will cause schools to increase their effectiveness (or value added) in helping children learn. This is because families will migrate away from schools with low value added and towards schools with high value added. Unfortunately, empirical analysis of voucher systems has found mixed results. In some settings, vouchers have boosted learning (e.g., Colombia), while in others they have actually caused it to decline (e.g., Louisiana). Explain this disparate set of results. Under what conditions will competition cause schools to increase their value added? How is it possible that this happens in some settings but not others?

Chandra et al. (2021)  Chandra et al. (2024) studies the health consequences of patient cost sharing. (a) Describe the natural experiment that the paper exploits. (b) What implications does the paper have for the optimal design of health insurance?