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?

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

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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