Question

Slope and the maximum height of a curve

This problem gives you a preview of something you might see in a microeconomics class. Suppose there’s an appliance store that sells air conditioners. It could set its price high and sell very few air conditioners, or it could set its price low and sell many more air conditioners. The following table shows some possible choices this store could make:

Price (Dollars per air conditioner) 400 300 200 Quantity (Air conditioners per year) Total Revenue (P x Q) (Dollars per year) C) C) 200 300 400 0,00 40,000 0,00 C) C)

The graph below plots the firm’s total revenue curve: that is, the relationship between quantity and total revenue given by the two right columns in the table above. The five choices are also labeled. Finally, two black lines are shown; these lines are tangent to the green curve at points B and D.

Using the information on the slope of the lines tangent to the curve at points B and D, plot the slope of the total revenue curve on the graph below. (As it turns out, it’s a straight line, so the two points you plot will determine a line.)

The total revenue curve reaches its maximum at a quantity of (400, 200, 100, 300)  air conditioners per year. At this point, the slope of the total revenue curve is (negative, equal to zero, positive, at its maximum, at its minimum) .

Answer 1

At point B the slope of the line = ($40000 - $20000) / (150 - 50) = 200

At point D the slope of the line = ($20000 - $40000) / (350 - 250) = -200

The total revenue curve reaches its maximum at a quantity of 200 air conditioners per year because at that level of output TR is maximum which is shown in the table. At this point, the slope of the total revenue curve is equal to zero.

Answer 2

The total revenue curve reaches its maximum at a quantity of 200 (point C) air conditioners per year. At this point the slope of the total revenue curve is Zero.

Explanation: As we can see from the above graph the value gets maximized at a price of $200 and when we increase the price or decrease the price the TR gets reduced.

From this we can say the revenue will decline when price is higher or lower than $ 200.

In other words when Marginal revenue is maximum then as per the maximization condition the first derivative that is slope must be equal to zero.