Question

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

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: 

Quantity Total Revenue (P x Q) Price (Dollars per air conditioner) (Air conditioners per year) (Dollars per year) 720 100 54,000 540 72,000 360 200 180 300 54,000 400 

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, point the slope of the total revenue curve on the graph below.

(As it tums 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  conditioners per year. At this point, the slope of the total revenue curve is

Answer 1

Slope of a curve reflects the direction and steepness of the curve at a certain point on the curve. It is the rate at which one variable is substituted for another. It is calculated as follows: Here, (xi, yi) and (x2, y2) are any two points on the tangent to the curve Total Revenue (TR) is the total amount of money earned from the sale of entire output at the market price The slope of TR at point B is equal to the slope of the tangent line at point B (the slope of a line is constant). To find the slope at point B, calculate the slope of the tangent line. The two co-ordinates of the tangent line are (50, 36,000) and (150, 72,000): 0%-v.) (X2-X1) (72,000-36,000) (150-50) 36,000 100 360 Hence, the slope of the TR curve at point B is '360' To find the slope at point D, calculate the slope of the tangent line at point D. The two co-ordinates of the tangent line are (250, 72,000) and (350, 36,000):

(V2-Vi) (36,000-72,000) (350-250) 36,000 100 -360 Hence, the slope of the TR curve at point D is '360' The two co-ordinates (quantity on x-axis, slope of y-axis) required to plot the slope of TR on a two-dimensional graph are (100, 360) and (300, -360). The slope of TR is plotted as follows: 450 360 270 180 90 OB(100, 360) Slope of TR -180 270 -360 450 D(300, -360) 50 100 150 200 250 300 350 400 QUANTITY (Air conditioners per year)

The total revenue curve is at its maximum at point C ($72.000, where the quantity of air conditioners per vear is 200 units If a tangent is drawn at point C, it will be a horizontal straight line. This means that there is no change in total revenue at this point (C Hence, the slope of the tangent line drawn at point C is equal to zero i.