Question

Suppose that a Örm faces a demand curve that has a constant elasticity of 2. This demand curve is given by q = 256=P2. Suppose also that the

Örm has a marginal cost curve of the form MC = 0:001q.
a) Graph these demand and marginal cost curves.
b) Calculate the marginal revenue curve associated with the demand
curve; graph the curve.
c) At what output level does marginal revenue equal marginal cost?

Answer 1

Demand equtionn: q = 256/P²

=> P² = 256/q

=> P = (256/q)^1/2

=> P = 16 /q^1/2 .

q	P
1	16
4	8
9	5.33
16	4

]

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Marginal cost curve: MC = 0.001q

q	MC
100	0.1
200	0.2
300	0.3
400	0.4
500	0.5
600	0.6
700	0.7
800	0.8
900	0.9
1000	1

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(b)

Demand equtionn: q = 256/P²

=> P² = 256/q

=> P = (256/q)^1/2

=> P = 16 /q^1/2 .
------------

TR = Pq

=> TR = (16 /q^1/2 ) * q

=> TR = 16q^1/2.

----

MR = ΔTR / Δq

=> MR = (16) (1/2) q^1/2-1

=> MR = 8 q^-1/2

=> MR = (8 / q^1/2 ).

q	MR
100	0.80
200	0.57
300	0.46
400	0.40
500	0.36
600	0.33
700	0.30
800	0.28
900	0.27
1000	0.25

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(c) Set MR = MC
=> (8/q^1/2) = 0.001q

=> (8/0.001) = q^1/2 * q

=> 8000 = q ^3/2

=> q = (8000) ^2/3

=> q = 400

At 400 units of output, MR=MC