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:
-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.
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.
To analyze the circumstances in which distributing free needles is a beneficial or bad policy, we need to understand the price responsiveness of both HIV/AIDS transmission rates and drug use.
1. Elasticity of HIV/AIDS spread with respect to the price of needles (Pn):
To compute the elasticity, we need equilibrium prices and quantities. Given the supply and demand functions for HIV/AIDS transmission:
SHIV/AIDS = 100 + 2Pn + Pd (supply function)
Ddrugs = 50 - Pn - Pd (demand function)
At equilibrium, both the quantity supplied and demanded are equal:
100 + 2Pn + Pd = 50 - Pn - Pd
To calculate the equilibrium price of needles (Pn), we need to rearrange the equation:
3Pn + 2Pd = -50
Now we can differentiate the supply function with respect to Pn to calculate the price elasticity of HIV/AIDS spread:
d(SHIV/AIDS)/dPn = 2
The price elasticity of HIV/AIDS spread (Ep) is constant and equal to 2, implying that a 1% increase in the price of needles leads to a 2% decrease in the spread of HIV/AIDS.
2. Elasticity of drug use with respect to the price of needles (Pn):
Following the same process, we differentiate the demand function for drugs with respect to Pn:
d(Ddrugs)/dPn = -1
The price elasticity of drug use (Ed) is constant and equal to -1, meaning that a 1% increase in the price of needles leads to a 1% decrease in drug use.
Now let's use these elasticities to assess the circumstances in which distributing free needles is a beneficial or bad policy:
a. Beneficial policy:
If we distribute free needles, the price of needles (Pn) effectively becomes zero, which implies an infinite decrease in price. With an Ep of 2, this will lead to a 200% reduction in HIV/AIDS spread, assuming all other factors remain constant. Consequently, distributing free needles becomes a beneficial policy when the reduction in HIV/AIDS spread outweighs the potential negative consequences associated with increased drug use.
b. Bad policy:
A potential downside of distributing free needles is that it might decrease the price of needles, reducing the perceived cost of drug use. With an Ed of -1, this implies a 100% increase in drug use. If this increase in drug use outweighs the reduction in HIV/AIDS spread, distributing free needles is considered a bad policy.
In summary, the circumstances under which distributing free needles is beneficial or bad depend on the relative magnitudes of the elasticities of HIV/AIDS spread (Ep) and drug use (Ed), as well as the potential impact on the overall societal well-being.