Mathematical approach to revenue and cost functions, Managerial Economics

A MATHEMATICAL APPROACH TO REVENUE AND COST FUNCTIONS

Recall that TR = P x Q

This implies that P(AR) = TR

                                    Q

For example, assuming that the AR function is given by:

AR = 20 - 1 Q

              3

TR = P x Q

     = 20Q - 1 Q2

                  3

Marginal revenue is  measure of the instantaneous rate of change of total revenue with respect to output Q.  (Refer to the basic rules of differentiation in Appendix 1 of Modern Economics by Mudida)

                                                MR = d TR

                                                         d Q

Thus, for example, given the following TR function:

                                                TR = 2Q - 1 Q 2

                                                               2        

                                                    AR = 2 - 1 Q

                                                                  2

                                                MR = d TR

                                                        d Q                               

                                                       = 2 - Q

The cost concepts studied earlier can also be expressed in functional form.  Cubic functions are commonly used to represent cost functions.  For example, a cost  function may take  the form:

TC = a + b Q + c Q 2 + d Q 3

Average cost refers to the cost per unit of output.

                  AC = TC

                           Q

                                          =  a + b + cQ + dQ 2

                                               Q

Marginal cost refers  to the instantaneous rate of change of the total cost function with respect to  output.

                                    MC = d TC     

                                             d Q 

Given  TC = a + bQ  + CQ2 + dQ 3

               MC = d TC

                         dQ

                   = b + 2 cQ + 3dQ 2

For example, given a total cost function

TC = Q3 - 8Q2 + 68Q + 4

MC = d TC = 3Q2 - 16Q + 68

         d Q

Posted Date: 11/28/2012 5:45:26 AM | Location : United States





Given that TC=1000+10Q-0.9Q^2+0.04Q^3 ,, find the rate of output Q that results in minimum Average variable cost
Posted by hillary | Posted Date: 7/3/2013 5:33:59 AM


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