Solve the problem.
-If the marginal price units of demand per week is proportional to the price p, and if at $80 there is no weekly demand [p(0) = 80], and if at $50.18 there is a weekly demand of 8 units [p(8) = 50.18], find the
Price-demand equation.

Question

Solve the problem.
-If the marginal price  units of demand per week is proportional to the price p, and if at $80 there is no weekly demand [p(0) = 80], and if at $50.18 there is a weekly demand of 8 units [p(8) = 50.18], find the
Price-demand equation.

Quizplus · Accepted Answer

We know from the problem that the marginal price is proportional to the price. So we can write:

m(p) = kp

Where m(p) is the marginal price in units of demand per week and k is the constant of proportionality.

Since at $80 there is no weekly demand, we know that the marginal price at that point is also 0:

m(80) = k(80) = 0

Solving for k, we get:

k = 0/80 = 0

So the marginal price equation becomes:

m(p) = 0p = 0

Now we can use the information that at $50.18 there is a weekly demand of 8 units:

m(50.18) = k(50.18) = 8

Substituting k = 0, we get:

m(50.18) = 0(50.18) = 0

This is a contradiction, since 0 cannot equal 8. Therefore, there is no such price-demand equation that satisfies the given conditions.

Solve the Problem. -If the Marginal Price Units of Demand Per Week