Question

The current equilibrium price and quantity in the market for walnuts are $5 per pound with 10,000 pounds supplied. Supermarkets are expecting to see sales rise to 15,000 pounds due to an unusually large crop of walnuts. If the price elasticity of demand is 1.8, what is the new price per pound of walnuts?
a. P = $5
b. P = $6
c. P = $4
d. P = $7

Answer 1

Answer:

Option (a) is correct.

Explanation:

Given that,

Initial Quantity supplied = 10,000

New quantity supplied = 15,000

Initial price = $5

Price elasticity of demand = 1.8

Percentage change in quantity supplied:

= [(New quantity supplied - Initial Quantity supplied) ÷ Initial Quantity supplied] × 100

= [(15,000 - 10,000) ÷ 10,000] × 100

= (5,000 ÷ 10,000) × 100

= 50%

Let the new price be x,

Percentage change in price:

= [(New price - Initial price) ÷ Initial price] × 100

= [(x - $5) ÷ $5] × 100

= (x - 5) × 20

= 20x - 100

Therefore,

Price elasticity of demand = Percentage change in quantity supplied ÷ Percentage change in price

1.8 = 50 ÷ (20x - 100)

1.8 (20x - 100) = 50

36x - 180 = 50

36x = 230

x = 5

Hence, the new price per pound of walnuts is $5.