ECON 157 Midterm Solution
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Question 1 (45 points)
Consider a situation where a population of consumers is deciding whether or not to buy a street
drug called Bearoin. A researcher observes these consumers’ purchases over two years, 1 and 2. The
price of Bearoin changes from year 1 to year 2, as a result of an increased number of sellers in the
market. The researcher observes the following prices of the drug, and quantities sold, in year 1 and
The year 1 price of the drug for consumers is P1 = $80. The year 1 quantity consumed at that price
is Q1 = 400
1. (5 points) Write down the formula for arc price elasticity of demand in terms of P1, Q1, P2,
2. (10 points) What is the arc price elasticity of demand for Beroin?
3. (10 points) Now consider a second, new population of consumers buying the same drug in
another location. In this new market:
The year 1 price of the drug for consumers is P1 = $80. The year 1 quantity consumed
at that price is Q1 = 240
The year 2 price of the drug for consumers is P2 = $20. The year 2 quantity consumed
at that price is Q2 = 1000
What is the arc price elasticity of demand for consumers in this second market?
4. (10 points) Now, there is a music festival where both of these populations come together and
form one population. They have the same demand for Bearoin at the prices listed above in
each market. What is the arc elasticity of demand for this combined population of consumers?
5. (10 points) The researcher now wants to use the arc elasticity computed for this combined
population to determine what the quantity sold of the drug would be if she could enact a
government crackdown so that the price of the drug at the festival rose from $20 to $120.
Using the arc elasticity computed above, and the quantities given above for P = 20, compute
the quantity that will be purchased under this new price.