Currently, at a price of $0.50 each, 250 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 $0.50 to $1 is unit-elastic (Es = 1). In the long run, a price increase from $0.50 to $1 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 $1 each? b. So how many popsicles will be sold per day in the long run if the price rises to $1 each?

Currently, at a price of $0.50 each, 250 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 $0.50 to $1 is unit-elastic (Es = 1). In the long run, a price increase from $0.50 to $1 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 $1 each?

b. So how many popsicles will be sold per day in the long run if the price rises to $1 each?

 

 

Answer:

a.

In the short-run:

Let Q2 be the required new quantity because of price rise.

Price elasticity of supply = [(Q2 – Q1)/{(Q1 + Q2)/2}] / [(P2 – P1)/{(P1 + P2)/2}]

1             = [(Q2 – 250)/{(250 + Q2)/2}] / [(1 – 0.50)/{(0.50 + 1)/2}]

250 + Q2 = 3Q2 – 750

2Q2 = 1,000

Q2 = 500

Answer: 500 units will be sold if the price rises to $1.

b.

In the long-run:

Let Q2 be the required new quantity because of price rise.

Price elasticity of supply = [(Q2 – Q1)/{(Q1 + Q2)/2}] / [(P2 – P1)/{(P1 + P2)/2}]

1.50        = [(Q2 – 250)/{(250 + Q2)/2}] / [(1 – 0.50)/{(0.50 + 1)/2}]

375 + 1.5Q2 = 3Q2 – 750

1.5Q2 = 1,125

Q2 = 750

Answer: 750 units will be sold if the price rises to $1.

Asked on February 15, 2018 in economics.
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