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The Johnson Robot Company’s marketing managers estimate that the demandcurve for the company’s robots in 2008 isP = 3,000 - 40Qwhere P is the price of a robot and Q is the number sold per month. Derive the marginal revenue curve for the firm and determine the marginal revenue for the 10th unit of output. a.$2200 b.$2600 c.$40 d.$80

Question

The Johnson Robot Company’s marketing managers estimate that the demand

curve for the company’s robots in 2008 is

= 3,000 - 40Q

where is the price of a robot and is the number sold per month.

 

Derive the marginal revenue curve for the firm and determine the marginal revenue for the 10th unit of output.

  a.

$2200

  b.

$2600

  c.

$40

  d.

$80

check_circleAnswer
Step 1

For the aforementioned question, the correct alternative is A and MR curve for the firm is MR = 3, 000 – 80Q

Step 2

Here, the demand curve for robots is:

P = 3,000 – 40Q

Therefore, the total revenue can be calculated as:

TR = Price of robots * Quantity of robots

TR = (3,000 – 40Q) * Q

TR = 3, 000 Q – 40Q2

Furthermore, MR = ΔTR/ΔQ

Thus, the equation for marginal revenue curve or MR curve becomes

MR = 3, 000 – 80Q

Now, estimate the MR from 10th unit of robots – there is a relation between MR and TR which states MR = TRn – TRn-1. From this it can be noted that MR from 10th unit = TR from 10th unit – TR from 9th unit, i.e.,

TR from 10th unit = 3, 000 (...

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