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CalculusQ&A LibraryTotal revenue is in dollars and x is the number of units.Suppose that in a monopoly market, the demand function for a product is given by p = 430 − 0.2xwhere x is the number of units and p is the price in dollars. (a) Find the total revenue from the sale of 500 units.(b) Find the marginal revenue MR at 500 units. Is more revenue expected from the 501st unit sold or from the 701st?Question

Asked Mar 5, 2019

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Total revenue is in dollars and x is the number of units.

Suppose that in a monopoly market, the demand function for a product is given by

p = 430 − 0.2x

where x is the number of units and p is the price in dollars.

(a) Find the total revenue from the sale of 500 units.

(b) Find the marginal revenue *MR* at 500 units.

Is more revenue expected from the 501st unit sold or from the 701st?

Step 1

*Given:*

The demand function is *p = *430*−*0.2*x*.

Step 2

(a)

Obtain the total revenue of 500 units.

*Calculation:*

In general the revenue function is represented in the form of *R = px*, where *x* is the number of units sold.

Then the revenue function for the given demand function is *R = x*(430−0.2*x*).

Thus, the revenue function is *R = *430*x−*0.*2x*^{2}*.*

Substitute *x* = 500 in *R = *430*x−*0.*2x*^{2}*.*

*R = *430(500)−0.2(500)^{2}*.*

= 215,000−50,000

= 165,000.

Thus, the total revenue obtained from the sales of 500 unit is $165,000.

Step 3

(b)

Compute the marginal revenue at 500 units.

*Calculation:*

The rate of change of the revenue function is the marginal revenue.

D...

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