2.5  Marginal Analysis and Approximations using Increments

 

Marginal Analysis

 

Marginal Cost  -  approximates the additional cost generated by producing one more.   C’(a) ~ C(a+1) – C(a)

 

Marginal Revenue  -  approximates the additional revenue generated by producing one more.    ** Remember R(x) = xp **

                                      R’(a) ~ R(a+1) – R(a)

 

Marginal Profit  -  approximates the additional profit generated by producing one more.      P’(a) ~ P(a+1) – P(a)

 

#4  If

 

pre a)  Find the revenue function.

 

 

 

 

a)  Find the marginal cost and the marginal revenue

 

 

 

 

 

 

b)  Use marginal cost to estimate the cost of producing the fourth unit.

 

 

 

 

c)  Find the actual cost of producing the fourth unit.

 

 

 

 

d)  Use marginal revenue to estimate the revenue derived from the sale of the fourth unit.

 

 

 

 

e)  Find the actual revenue derived from the sale of the fourth unit.

 

 

 

 

 

 

#12  MARGINAL ANALYSIS

A manufacturer’s total monthly revenue is  dollars when q units are produced and sold during the month.  Currently, the manufacturer is producing 80 units a month and is planning to increase the monthly output by 1 unit.

 

a)  Use marginal analysis to estimate the additional revenue that will be generated by the production and sale of the 81st unit.

 

 

 

 

 

 

 

 

b)  Use the revenue function to compute the actual additional revenue that will be generated by the production and sale of the 81st unit.

 

 

 

 

 

 

 

 

 

Approximation by Increments

 

          The approximate change in f(x) at  and , a small change in x  is      

 

 

 

#8  Estimate how much the function   will change as x decreases from 4 to 3.8.

 

 

 

 

 

 

 

 

 

#16  MANUFACTURING

A manufacturer’s total cost is   dollars when the level of production is q units.  The current level of production is 4 units, and the manufacturer is planning to increase this to 4.1 units.  Estimate how the total cost will change as a result.

 

 

 

 

 

 

+-

 

 

#18 EFFICIENCY

          An efficiency study of the morning shift at a certain factory indicates that an average worker arriving on the job at 8:00 a.m. will have assembled   transistor radios x hours later.  Approximately how many radios will the worker assemble between 9:00 and 9:15 a.m.

 

 

 

 

 

 

 

 

 

 

 

 

Approximation Formula for Percentage Change

 

         

 

GROSS DOMESTIC PRODUCT 

The gross domestic product of a certain country was   billion dollars t years after 1995.  Use calculus to predict the percentage change in the GDP during the first quarter of 2003.