Determine the change in revenue in the given cases: The marginal revenue function for a firm’s product is MR = -0.04x + 10 where x equals the number of units sold. Determine the total revenue from selling 200 units of the product and what is the added revenue associated with an increase in sales from 100 to 200 units.

Expert Answers

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The marginal revenue is the revenue earned for each extra product sold. If the revenue earned when x number of products is sold is R(x), MR = R'(x).

MR = -0.04x + 10

The revenue earned when 200 units are sold is:

`int_(0)^200 -0.04x + 10 dx`

=> `-0.02x^2 + 10x` from 0 to 200

=>` -0.02(200^2 - 0) + 10*(200 - 0)`

=> 2000 - 800

=> 1200

The increase in revenue from 100 products to 200 products is:

`int_(100)^200 -0.04x + 10 dx`

=>` -0.02x^2 + 10x` from 100 to 200

=> `-0.02(200^2 - 100^2) + 10*(200 - 100)`

=> 1000 - 600

=> 400

The revenue associated with the sale of 200 units is 1200 and the increase in revenue when 200 units are sold instead of 100 is 400.

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