**Assume that the demand function for a certain commodity had the following form where x is the quantity demanded, measured in units of a thousand and p is the unit price in dollars.**

**p = sqrt(-ax^2 + b) text( where ) (a>=0,b>=0)**

**Suppose the quantity demanded is 6000 (x = 6) when the unit price is $8.00 and 8000 (x = 8) when the unit price is $6.00. Determine the demand equation**

**Answer:**

Given x= 6 when P= 8

also x= 8 when P= 6

Substituting these in given demand- price equation we get

8 = sqrt(- 36a +b)

6 = sqrt(- 64a +b)

Taking square on both sides we get

64 = -36a + b -(1)

36 = -64a + b -(2)

Subtracting eq(2) from eq(1), we get

28 = 28a

a=1

Substituting this in equation 1, we get

b= 100

Therefore

P=sqrt(-x^2+100)

P^2= -x^2 + 100

x = sqrt(100 - P^2)

This is the required demand equation.