Question

A monopoly believes that demand for its good is linear. They also believe that they can sell ten units of their good when the market price is 120 and 20 units when the price is 70. Let each potential customer in the market buy, at most, one unit of the good. Write down the monopoly’s inverse demand function.

Answer 1

General demand function : Q = a+bP

When P = 120 :: Q = 10

putting this value into general demand function

10 = a + 120b --------------------Equation 1

When P = 70 :: Q = 20

putting this value into general demand function

20 = a + 70b ---------------------Equation 2

subtracting 1 and 2 eqn, we get

10 = a + 120b -(20 = a + 70b)

b = -(1/5)

Putting this value into equation 1,

10 = a + 120(-1/5)

a = 34

Putting this value into general demand function

Q = 34 - (1/5)P

inverse demand function

P = 170 - 5Q