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 price increase from $1 to $2 is unit-elastic (Es = 1). In the long run, a price increase from $1 to $2 has an elasticity of supply of 1.50. (Hint: Apply the midpoints approach to the elasticity of supply.)

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

Answer 1

Answer: A. short run quantity = 167 b. long run quantity = 200.000

Step-by-step explanation:

A.short run

When price increases from $1 to $2 the Elasticity of supply is 1. A unit elasticity tells that a 1% percentage change in prices will cause an equal 1% change in the quantity supplied.

The percentage price change = $2 - $1/(($2 + $1)÷2) = $1/$1.5 = 0.666666

The percentage price change = 66.67%

When the price changes from $ 1 to $2 the percentage change is 66.67% , given the unit elasticity of supply, the quantity supplied will increase by 6.67%. The quantity of Popsicles supplied will be 100 x 1.6667= 166.67 ≈ 167.

B. long run

The elasticity of supply in the long run is 1.50, meaning a 1% increase in the price of popsicles will cause a 1.50 percentage increase in the quantity of Popsicles supplied

The percentage price change = $2 - $1/(($2 + $1)÷2) = $1/$1.5 = 0.666666

The percentage price change = 66.67%

the price elasticity is 1.50 meaning a 66.67% increase in price will cause a 100.005% (66.67 x 1.50) increase in the quantity of popsicles supplied

quantity supplied equal 200.005 (100 x 100.005% + 100) ≈ 200