Question

The revenue in dollars generated from a sale of x picnic tables is given by R(x)=26x -x²/500 Answer parts (a) through (d). 

(a) Find the marginal revenue when 2000 tables are sold. 

(b) Estimate the revenue from the sale of the 2001st table by finding R'(2000). 

(c) Determine the actual revenue from the sale of the 2001st table. 

(d) Compare your answers for parts (b) and (c). What do you find? 

Answer 1

Answer

a)

R(x) = 26x - x²/500

R ' (x) = 26 - x/250

Marginal Revenue = R ' (x) and here we have x = 2000

=> Marginal Revenue when 2000 tables are sold = R ' (2000) = 26 - 2000/250 = 18

b)

Marginal revenue is defined as the increase in revenue for additional marginal increase in Output. Hence, The estimate of the revenue from the sale of 2001st table by finding R ' (2000) is $18

c) Formula:

Revenue from nth table = Revenue from n tables - Revenue from (n - 1) tables  

=>Revenue from 2001st table = Revenue from 2001 tables - Revenue from 2000 tables  

= R (2001) - R(2000)

Hence the correct answer is (A) R (2001) - R(2000)

Now,

R (2001) - R(2000) = 26*2001 - 2001²/500 - ( 26*2000 - 2000²/500)

=17.998

Actual revenue from the 2001st table is $17.998

d)

We can see that Answer in part (b) and (c) are almost equal.

Hence we can say that Marginal Revenue gives a similar approximation of the actual revenue from the sale of the 2001st table because the marginal revenue is the derivative of the actual revenue.