1 Salight Inc. manufactures and sells sailboards. Management has evidence that t
ID: 1141814 • Letter: 1
Question
1 Salight Inc. manufactures and sells sailboards. Management has evidence that the price clasticity of demand is - 3.0. Currently, boards are priced at S500 and the quantity demanded is 10,000 per year. If the price is increased to $700, how many sailboards will the company be able to sell cach year? (Hint: Make use of the clasticity reported in the problem statement, set it equal to the arc clasticity formula, and the result will be one cquation in one unknown.) a. Formula used: Items given and their values: Your work: Answer b. How much and in what direction will total revenue change due to the price increase?Explanation / Answer
ANSWER:
A) ped = -3
initial price (p1) = $500
initial quantity demanded (q1) = 10,000
increased price (p2) = $700
quantity demanded after price increase (q2) = ?
ped = (q2 - q1) / q1 / (p2 - p1) / p1
-3 = (q2 - 10,000) / 10,000 / (700 - 500) / 500
-3 = (q2 -10,000) / 10,000 / 200 / 500
-3 = (q2 - 10,000) * 500 / (10,000 * 200)
-3 = (500q2 - 5,000,000) / 2,000,000
-3 * 2,000,000 = 500q2 - 5,000,000
-6,000,000 = 500q2 - 5,000,000
-6,000,000 + 5,000,000 = 500q2
-1,000,000 = 500q2
q2 = -1,000,000 / 500
q2 = -2,000
so the quantity demanded is 2,000
b) total revenue change = new total revenue - old total revenue
total revenue change = $700 * 2,000 - $500 * 10,000
total revenue change = $1,400,000 - $5,000,000
total revenue change = -$3,600,000
so the revenue decreases by $3,600,000 as the price goes up.
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