There is a debate about whether sterile needles should be given out in cities with high drug use. Some say that doing so will decrease HIV/AIDS from sharing needles. Others believe it will encourage drug use. As an economist, you must know the following:

Question

-How responsive the spread of HIV/AIDS is to the price of needles
-How responsive drug use is to the price of needles

Assuming you know these, use the concepts of price elasticity of demand for sterile needles, and the cross-price elasticity between drugs and sterile needles to answer the following:
a. In what circumstances do you believe distributing free needles is a beneficial policy?
b. In what circumstances do you believe distributing free needles is a bad policy?

Redo the above given the following:
SHIV/AIDS = 100 + 2Pn + Pd (supply function)
Ddrugs = 50 - Pn - Pd (demand function)

Pn = price of needles
Pd = price of drugs

Assume that HIV/AIDS is transmitted and spread entirely through drug use.

*All I know is that you have to compute the relevant point measures of elasticity at equilibrium prices.

Answer 1

First off, check your HIV supply equation. I would think HIV and Pd would be negatively correlated. If Pd goes up, drug use goes down and thus the quantity of needles goes down, thereby lowering HIV.

Anyway. I see several issues with your question. First, with the linear equations, HIV supply elasticity and drug demand elasticity are not constant. As HIV increases, the elasticity of HIV goes down. Second, you are not given Pn or Pd or ways to calculate Pn or Pd. So you cannot determine a baseline equilibrium for HIV or drugs. Third, you do not have any social costs of HIV or drug usage. The policy questions involve the trade-off between more drugs and less HIV vs more HIV and less drugs. For example, if HIV has an extremely high social cost and drugs do not, then any policy that reduces HIV is a beneficial policy; regardless of the elasticities.

Ok, so here is my answer. If the demand for drugs is highly inelastic and the supply of HIV is relatively elastic, then free needles is (probably) a beneficial policy; you get HIV reduction without much increase in drug usage.