For a monopoly firm, the marginal revenue of the first unit of output sold is Rs 36 and MR is zero when the output is 12. What is the equation of the AR curve?

$A R = 12 - \frac{q}{3}$

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$A R = 12 - \frac{q}{6}$

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$A R = 36 - 3 q$

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$A R = 36 - 1.5 q$

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Solution

The correct option is D
$A R = 36 - 1.5 q$

When q=0, MR =36 and when q=12, MR =0
It can be seen that the equation of the MR curve is MR = 36 - 3q.
The slope of the MR curve is -3. Since the MR curve is twice as steep as the demand curve, the slope of the demand curve is -1.5.

Also, the MR curve and the demand curve start from the same point i.e. when q=0, p= Rs 36.
Hence, the equation of the demand curve is p=36- 1.5q.

Also, since average revenue is equal to the price, AR curve is the same as the demand curve. Hence, the equation of the AR curve is AR =36-1.5q

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