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Answer to Question #70460 in Microeconomics for Ariba

Question #70460
NEXT is contemplating a T-shirt advertising promotion. Monthly sales data from T-shirt shops
marketing the “Eye Watch NEXT” design indicate that
Q = 1,500 – 200P
Where: Q is T-shirt sales and P is price.
A. How many T-shirts could NEXT sell at $4.50 each?
B. What price would NEXT have to charge to sell 900 T-shirts?
C. At what price would T-shirt sales equal zero?
D. Calculate the point price elasticity of demand at a price of $5?
Expert's answer
How many T-shirts could NEXT sell at $4.50 each?

Q = 1,500 – 200*4.50=1,500-900=600

What price would NEXT have to charge to sell 900 T-shirts?

Q = 1,500 – 200P=900 when P=(1,500-900)/200=$3

At what price would T-shirt sales equal zero?

Q = 1,500 – 200P=0 when P=1,500/200=$7.50

D. Calculate the point price elasticity of demand at a price of $5?

The point price elasticity of demand is calculated as

K_d=dQ/dP×Р/Q
So,
K_d=(1,500-200P)^'×P/Q(P) =-200×5/(1,500-200×5)=(-1000)/500=-2

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