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- Date Submitted: 07/31/2016 8:29 PM
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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

year 2:

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,

and Q2.

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.

Question...