Deadweight Loss of Commodity Taxation

In March 2015, Berkeley became the first US jurisdiction to implement a soda tax. This question is designed to think about the impacts of this tax.

Let the price of soda in Berkeley be equal to P per ounce. Suppose each individual in Berkeley has a demand for beverages equal to Qdi = 10 20P, where Qdi is measured in ounces per person. Let total supply of soda be equal to QS = 8, 000, 000 ? P, which is measured in ounces for the whole market. Suppose there are 100, 000 people in Berkeley.

(d) Draw a supply-demand graph which shows the eject of the tax on quantities and prices. In the graph, identify the change in surplus to the buyers of soda, the change in surplus to the suppliers of soda, the change in government revenues, and the deadweight loss due to the tax. Calculate the deadweight loss (you do not have to calculate the other coe cients). There has been an established link between drinking sugary beverages and many health problems like heart disease. Suppose that each additional ounce of soda consumption costs the health system an average of .01$, and suppose these costs are entirely borne by the government.

(e) How much does the government save in avoided health costs? How does this compare to the deadweight loss to the tax you calculated in (d)? Does the tax increase total surplus?

(f) Now, suppose the government does not pay for medical care, and so individuals are responsible for paying for any increase in their own health costs. Does the tax increase or decrease total surplus now? Does your answer depend on whether you believe individuals act “rationally” or if they are subject to individual failures (the behavioural economics view)?