Question

Currently at a price of $1 each, 100 popsicles are sold per day in the perpetually hot town of Rostin. Consider the elasticity of supply. In the short run, a priceincrease from $1 to $2 is unit-elastic (Es=1.0).
In the long run, a price increase from $1 to $2 has an elasticity supply of 1.50.

So how many popsicles will be sold per day in the long run if the price rises to $2 each?

Answer 1

This question deals with the concept of elasticity in the long run as well as in the short run.
To solve this problem, we consider the mid point formula of elasticity.

The given data can be summarized as follows:

At a price of $1 each, 100 popsicles are sold per day in the perpetually hot town of Rostin.
In the short run, a price increase from $1 to $2, the supply is unit-elastic. (Es=1.0)

The mid point formula for elasticity is

On substitution, we get

we know that Es = 1; as it is unitary elastic, we substitute Es = 1 in the equation

Therefore in the short run, at the price of $2, 200 popsicles will be sold.

In the long run, the price elasticity is given as 1.50 and the price increases from $1 to $2.

Using the midpoint formula, we can get the price elasticity of supply.

As we know that Es = 1.5; we substitute Es = 1 in the equation.

Therefore in the long run, at $2, 300 pop sicles will be sold.