Question

2. Calculating marginal revenue from a linear demand curve 

The blue curve on the following graph represents the demand curve facing a firm that can set its own prices. 

Use the graph input tool to help you answer the following questions. You will not be graded on any changes you make to this graph. 

Note: Once you enter a value in a white field, the graph and any corresponding amounts in each grey field will change accordingly.

On the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 10, 20, 25, 30, 40, and 50 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results.

Calculate the total revenue if the firm produces 10 versus 9 units. Then, calculate the marginal revenue of the 10th unit produced. 

The marginal revenue of the 10th unit produced is $_______  . 

Calculate the total revenue if the firm produces 20 versus 19 units. Then, calculate the marginal revenue of the 20th unit produced. 

The marginal revenue of the 20th unit produced is $_______ . 

Based on your answers from the previous question, and assuming that the marginal revenue curve is a straight line, use the black line (plus symbol) to plot the firm's marginal revenue curve on the following graph. (Round all values to the nearest increment of 30.)

Comparing your total revenue graph to your marginal revenue graph, you can see that when total revenue is decreasing, marginal revenue is _______ .

Answer 1

Working notes:

(I) Equation of Linear demand function: P = a - bQ.

From demand graph:

When Q = 0, P = 150

150 = a - 0 x b

a = 150 (vertical intercept)

When Q = 50, P = 0.

0 = a - 50b

0 = 150 - 50b

50b = 150

b = 3

So, Equation of Linear demand function: P = 150 - 3Q

(II) Total revenue (TR) = P x Q = 150Q - 3Q²

So, Marginal revenue (MR) = dTR/dQ = 150 - 6Q

Therefore:

(A) Graph of Total revenue

Data:

Q	P	TR
0	150	0
10	120	1200
20	90	1800
25	75	1875
30	60	1800
40	30	1200
50	0	0

Graph:

1880 1692 Total Revenue TOTAL REVENUE (Dollars) 0 5 10 40 45 50 15 20 25 30 35 QUANTITY (Number of units)

(B) Using linear Demand equation derived: P = 150 - 3Q:

(i)

If Q = 9, P = 150 - 3 x 9 = 150 - 27 = 123, so TR = 123 x 9 = 1107

If Q = 10, TR = 1200 (using data table).

MR of 10th unit = $//img.homeworklib.com/questions/fe3daa40-79ec-11ea-8d39-add06b0099f8.png?x-oss-process=image/resize,w_560$ TR / $//img.homeworklib.com/questions/fee1cbe0-79ec-11ea-bfd5-651f1f6b6c80.png?x-oss-process=image/resize,w_560$Q = (1200 - 1107) / (10 - 9) = 93/1 = 93

(ii)

If Q = 19, P = 150 - 3 x 19 = 150 - 57 = 93, therefore TR = 93 x 19 = 1767

If Q = 20, TR = 1800 (from data table)

MR of 20th unit = $//img.homeworklib.com/questions/ff7e3f00-79ec-11ea-84cd-3d452da0d526.png?x-oss-process=image/resize,w_560$ TR / $//img.homeworklib.com/questions/0017c780-79ed-11ea-acdc-b18de57b13ce.png?x-oss-process=image/resize,w_560$Q = (1800 - 1767) / (20 - 19) = 33/1 = 33

(3) Using MR equation derived: MR = 150 - 6Q

Data:

Q	P	MR
0	150	150
10	120	90
20	90	30
30	60	-30
40	30	-90
50	0	-150

Graph:

Marginal Reven MARGINAL REVENUE (Dollars) 0 5 10 15 25 20 25 30 QUANTITY (Units) 35 40 45 50

(4) When Total revenue is decreasing, Marginal Revenue is negative.