In the village of Frankfurter, the demand function for sausages per person is D(p) = 20 - 1.5p, where p is the price of a single sausage. The present population of Frankfurter is 100 persons. Suppose that 10 more people move into town, each of whom has the same demand function as the old residents. At a price of $2, the price elasticity of demand for sausages in Frankfurter is

Question

Quizplus · Accepted Answer

The price elasticity of demand is given by the formula:

E(p) = -(dQ/dp)(p/Q)

Where Q is the quantity demanded and dQ/dp is the derivative of the demand function with respect to price.

At a price of $2, the quantity demanded is:

D(2) = 20 - 1.5(2) = 17

Now suppose 10 more people move into town. The total population is now 110, and the new demand function is:

D(p) = 30 - 1.5p

At a price of $2, the quantity demanded is:

D(2) = 30 - 1.5(2) = 27

The percentage change in quantity demanded is:

((27-17)/17) x 100% = 58.8%

The percentage change in price is:

((2-2)/2) x 100% = 0%

Therefore, the price elasticity of demand at a price of $2 is:

E(2) = -(58.8%)/(0%) = undefined

Since the price elasticity of demand is undefined at a price of $2, it cannot increase, decrease, or remain unchanged. Therefore, the correct answer is C) unchanged.

In the Village of Frankfurter, the Demand Function for Sausages