Question

< Notes

A frim has the demand
in the form
function
p=a-bQ. The number of
units demanded is 60
when the price is RS.40
and 50 when the price is
RS.60. Find the values of
a,b and the demand
function.
...

Answer 1

p = 160 - 2Q

Explanation:

To find the values of 'a' and 'b' in the demand function p = a - bQ, we can use the given information about the demand at different price levels.

We are given two data points:

When the price (p) is RS.40, the quantity demanded (Q) is 60.

When the price (p) is RS.60, the quantity demanded (Q) is 50.

Using these data points, we can set up a system of equations to solve for 'a' and 'b'.

Equation 1: RS.40 = a - b(60)

Equation 2: RS.60 = a - b(50)

Let's solve this system of equations:

From Equation 1:

40 = a - 60b (multiply both sides by -1)

From Equation 2:

60 = a - 50b

Now, we have two equations with two variables. We can solve them simultaneously using any method (substitution, elimination, or matrices). Let's use the substitution method:

Substitute the value of 'a' from Equation 1 into Equation 2:

60 = (40 + 60b) - 50b

60 = 40 + 60b - 50b

60 = 40 + 10b

10b = 60 - 40

10b = 20

b = 20/10

b = 2

Now, substitute the value of 'b' back into Equation 1 to find 'a':

40 = a - 60(2)

40 = a - 120

a = 40 + 120

a = 160

Therefore, the values of 'a' and 'b' are a = 160 and b = 2.

The demand function can now be written as:

p = 160 - 2Q