Question

The demand for a new car for a month is 400 units when the Price is $ 16,700, and 500 units when the price is $ 14,900. Find the demand equation for cars, assuming that the relationship between price and Quantity is linear.

m = p2 - p1  
        q2 - q1

Answer 1

Total cost for 400 units = $16,700

Total cost for 500 units = $14,900

Here:

p1 = 16,700

p2 = 14,900

q1 = 400

q2 = 500

The demand curve is as follows:

Q = a + b(P)

Now we need to solve these two equations simultaneously:

q1 = a - b*p1

q2 = a - b*p2

Hence:

400 = a - b*16700

500 = a = b*14900

Solving we get as follows:

Hence the required demand equation is:

Q = a - 0.056*P

We need to find a,

We know that:

For Q = 400, P = 16,700

Hence,

substituting in Q = a - 0.056*P

we have:

a = 1327.778

Hence the required demand equation is:
Q = 1327.778 - 0.056*P