Question

Assume the demand function for SeatComfy's table chairs is Q = 5,000 -25P + 4I +10P_A-15P_T. Moreover, assume that currently P = 10, P_A = 15, I = 500, P_T = 100. Which of the following is true?

Select one:

A. If SeatComfy increases its price by 1 percent, sales as well as total revenues will decrease.

B. If SeatComfy decreases its price by 1 percent, sales will increase, while total revenues will decrease.

C. If SeatComfy increases its price by 1 percent, sales will decrease, while total revenues will increase.

D. If SeatComfy increases its price by 1 percent, sales as well as total revenues will increase.

Answer 1

The demand function is as follows -

Q = 5,000 - 25P + 4I + 10 PA - 15PT

P = 10

PA = 15

I = 500

PT = 100

Derive demand function with respect to price -

Q = 5,000 - 25P + 4I + 10 PA - 15PT

Q = 5,000 - 25P + (4 * 500) + (10 * 15) - (15 * 100)

Q = 5,000 - 25P + 2,000 + 150 - 1,500

Q = 5,650 - 25P

Calculate quantity demanded at given price

Q = 5,650 - 25P

Q = 5,650 - (25 * 10) = 5,650 - 250 = 5,400

The quantity demanded is 5,400 table chairs.

Calculate the price elasticity of demand -

Ed = [dQ/dP] * [P/Q]

Ed = [d(5,650 - 25P)/dP] * [10/5,400]

Ed = (-25) * [1/540]

Ed = -0.046

The elasticity of demand for SeatComfy's table chairs is -0.046

The value of elasticity of demand is less than 1.

So, the demand for SeatComfy's table chairs is inelastic.

In case of inelastic demand, an increase in price increases total revenue and a decrease in price leads to decrease in total revenue.

So,

If SeatComfy increases its price by 1 percent, sales will decrease, while total revenue will increase.

Hence, the correct answer is the option (C).