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


Related Discussions:- Mathematical approach to revenue and cost functions, Assignment Help, Ask Question on Mathematical approach to revenue and cost functions, Get Answer, Expert's Help, Mathematical approach to revenue and cost functions Discussions

Write discussion on Mathematical approach to revenue and cost functions
Your posts are moderated
Related Questions
"A budget deficit that is only temporary cannot be the source of inflation."  Is this statement true, false, or uncertain?  Describe your answer.


Define concept of Managerial decision-making Managerial decision-making draws on economic concepts as well as techniques and tools of analysis provided by decision sciences. T

A firm's technology needsit to combine 5 person-hours of labor with 3 machine-hours to make 1 unit of output. The firm has 15 machines in place and the wage rate rises from $10 per

Average Propensity to save The Average Propensity to Save [APS] is defined as the fraction of aggregate national income which is devoted to savings.  Thus if S denotes savin

Fall in Supply When the supply falls, the supply curve shifts to the left to position S 1 S 1 .  At the initial equilibrium price P 1 , quantity supplied falls from q 1

Supply and Demand Discuss and analyze following statement: The Wall Street Journal reported that recent law school graduates were having a very difficult time obtaining jo

Q. Explain about Utility analysis? A subset of consumer demand theory which analysis consumer behaviour and market demand employing marginal utility and total utility. Key prin

Infant Industry Argument Advocates of this maintain that if an industry is just developing, with a good chance of success once it is established and reaping economies of sale,

what is asset market theory theory in environmental economics?