Question

Given the following demand and supply equation for the furniture market.
D: P = 400 – 0.6Q S: P= 50 + 0.1Q
1- Calculate the equilibrium price and quantity.
2- Calculate price elasticity of demand as the price increases from 100$ to 150$. Interpret your
result.
3 – Use your result in the previous question to state weather this increase in price will lead to an
increase or decrease in the total revenue.
4 – Calculate total revenue at the price of 100$ and 150$ and prove your analysis in question 3.

Answer 1

1.

Equating D = S,

400 - 0.6Q = 50 + 0.1Q

0.7Q = 350

Q = 500

P = 50 + 0.1 x 500 = 50 + 50 = 100

2.

From demand function: P = 400 - 0.6Q, so Q = (400 - P) / 0.6

When P = 100, Q = (400 - 100) / 0.6 = 300 / 0.6 = 500

When P = 150, Q = (400 - 150) / 0.6 = 250 / 0.6 = 416.67

Using midpoint method,

Elasticity of demand (Ed) = (Change in Q / Average Q) / (Change in P / Average P)

= [(416.67 - 500) / (416.67 + 500)] / [(150 - 100) / (150 + 100)]

= (- 83.33 / 916.67) / (50 / 250)

= - 0.45

3.

Since |Ed| < 1, demand is inelastic. With inelastic demand, an increase in price will increase total revenue.

4.

Revenue (TR) = P x Q

When P = 100, TR = 100 x 500 = 50,000

When P = 150, TR = 150 x 416.67 = 62,500.5

So, higher price has increased revenue.