Question

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.

Answer 1

Solution:

At the tangency, slope of a curve is same as the slope of the line. So, to find the slope of Total revenue curve, we can use points B and D, and find the slope of the lines passing through the them.

From basic mathematics, we know

slope of a line = (y2 - y1)/(x2-x1). In the given graph, y-axis is marked by total revenue, TR, while the z-axis is marked by quantity, Q, so here slope becomes (TR2 - TR1)/(Q2 - Q1)

So, at point B, TR1 = $54,000 and Q1 = 100 ACs. Choosing any other point on the line (say, where the line ends), TR2 = $72,000 and Q2 = $150

Slope at point B = (72000-54000)/(150-100) = 18000/50 = 360

Similarly, at point D, TR1 = $54,000 and Q1 = 300 ACs. Other point chosen on line could again be the end point of the line, say TR2 = $36,000 and Q2 = 350 ACs.

Slope at point D = (36000-54000)/(350-300) = -18000/50 = -360

Joining the two points: (100, 360) and (300, -360) gives us the line/curve of slope of total revenue.

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Clearly from the graph of total revenue, we can see that the total revenue reaches it's maximum at point C, where quantity of ACs is 200 per year. From the second graph that we plotted (of slope of total revenue curve), we can see that at the quantity of 200 ACs, slope of TR is 0.