Question

Suppose a certain outlet chain selling appliances has found that for one brand of stereo system, the monthly demand is 240 when the price is $900. However, when the price is $850, the monthly demand is 315. Assuming that the demand function for this system is linear, write the equation for the demand function. Use p for price and q for quantity.

Answer 1

Answer: Therefore the demand function can be given as;

q = -3/2p + 1590

Explanation:

Given that at;

$900 the monthly demand is 240. ....1

$850 the monthly demand is 315. ....2

Since, the function is a linear function. The demand function would be of the form;

q = mp + c ....5

Where q = quantity demanded

p = price m = slope and c = intercept

Substituting conditions 1 and 2 to the equation.

240 = 900m + c. ...3

315 = 850m+ c ...4

Subtracting eqn 4 from 3

-75 = 50m

m = -75/50

m = -3/2

Substituting m = -3/2 into equation 3;

We have,

240= -3/2(900) + c

c = 240 + 3/2(900)

c = 1590

Therefore the demand function can be given as; substituting m and c into equation 5, we have;

q = -3/2p + 1590