Question

You are division manager at Toyota. If your marketing department estimates that the semiannual demand for the Highlander is Q = 100,000 – 1.25P, what price should youcharge in order to maximizes revenues from sales of the Highlander?

Answer 1

“Total revenues” of a firm are the total amount of revenues earned by selling quantities (Q) of a product in the market at market equilibrium price level (P).

It is calculated as follows:

The total revenue curve initially increases at an increasing rate. This means that, initially, the total revenues increase when the production level increases (positive slope).

With a further increase in the output level, the total revenues increase at a decreasing rate and reach a maximum point.

At this point, the slope of the total revenue curve becomes “zero”. After reaching maximum point, the total revenue curve starts to fall (the slope becomes negative).

The demand curve is given as follows:

The inverse demand function is written as follows:

The total revenues of the firm ‘T’ are as follows:

Derivate the total revenue function with respect to output level ‘Q’ in order to find the slope of the total revenue curve.

Further, equate the resulting function (known as marginal revenue function) to “zero” in order to find the maximum point of the total revenue function.

This is shown below:

Thus, the quantity which maximizes the total-revenue is 50,000 units.

The price level is calculated below as follows:

Thus, the price level which maximizes the total revenues of the firm ‘T’ is $40,000.

The total revenues are maximized when the price is set at $40,000 and 50,000 units are produced.

This could be verified by taking a second derivative of the total revenue function as follows:

As the second order derivative has turned out to be “negative”, this implies that the total revenues are maximized when the price of “Highlander” is $40,000.