Question

For a price-searcher, assume the demand curve is Q = 10 - P.

a.)        Construct a four-column table of P and Q with P ranging from 10 to 0. Calculate TR and MR and add them to your table.

b.)       Graph D and MR. (Plot points—with $ on the vertical axis and Q on the horizontal axis.

c.)        Why is P > MR (after the first unit)—or in other words, what is the good news and bad news for the price searcher as Q increases?

Answer 1

a) Complete the table as follows:

P	Q	TR	MR
0	10	0	--
1	9	9	9
2	8	16	7
3	7	21	5
4	6	24	3
5	5	25	1
6	4	24	(-1)
7	3	21	(-3)
8	2	16	(-5)
9	1	9	(-7)
10	0	0	(-9)

Here, TR = P x Q

MR =

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b)

Here, the MR curve crosses the x-axis between the 4th and 5th unit of output.

For the demand curve, x-intercept is 10 units, and y-intercept is $10.

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c) As Q increases, P falls.

P > MR after the first unit. With every extra unit produced, the MR begins to fall.

This is because TR increases only till the 5th unit, and then begins to fall again.

The good news for the price searcher is that as Q increases, TR will gradually increase. The bad news is that TR will begin to fall again, after the 5th unit. After this, MR becomes negative.

The firm cannot raise prices, and can neither raise quantity, indefinitely. It has to find the optimal point.

The firm has to maximize total revenue, and minimize total costs. Thus, it should not operate in the zone where MR is negative.