Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(3) C= 10+20q+4q 2.

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Presentation transcript:

Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(3) C= 10+20q+4q 2

Mathematical Cost Functions - 3 A Tabular Solution C= 10+20q+4q 2 Compute TC, AC, and MC when q=10 Find where MC = AC What level of output minimizes AC? When is MC = 60?

Mathematical Cost Functions - 3 A Tabular Solution

Mathematical Cost Functions - 3 A Tabular Solution C = 10+20q+4q 2

Mathematical Cost Functions - 3 A Tabular Solution C = 10+20q+4q 2 C = (3) +4 (3 2 )

Mathematical Cost Functions - 3 A Tabular Solution C = 10+20q+4q 2 C = (3) +4 (3 2 ) C = C = 106

Mathematical Cost Functions - 3 A Tabular Solution AC(3) = 106/3 =35.3

Mathematical Cost Functions - 3 A Tabular Solution MC(4) = = 48

Mathematical Cost Functions - 3 A Tabular Solution Compute TC, AC, & MC when Q = 10

Mathematical Cost Functions - 3 A Tabular Solution Find where MC = AC What level minimizes AC?

Mathematical Cost Functions - 3 A Tabular Solution Where is MC = 60?

Mathematical Cost Functions - 3 A Second Problem C = q 2 Compute TC, AC and MC when q = 10 Find the value of q where MC = AC What level of q minimizes AC When is MC = 60?

Mathematical Cost Functions - 3 A Second Problem C = q 2 Compute TC, AC and MC when q = 10 TC = 1005; AC = 100.5; MC =200 Find where MC = AC. q = What level of q minimizes AC? q = When is MC = 60? q= 3

Mathematical Cost Functions - 3 A Second Problem The answers are based on the equations. You should also solve the problem using the table.

Mathematical Cost Functions - 3 Fixed and Variable Cost We divide the firm’s costs into fixed and variable components.

Mathematical Cost Functions - 3 Fixed and Variable Cost We divide the firm’s costs into fixed and variable components. Fixed costs, FC, are those the firm would incur if it had no output; FC = C(0).

Mathematical Cost Functions - 3 Fixed and Variable Cost We divide the firm’s costs into fixed and variable components. Fixed costs, FC, are those the firm would incur if it had no output; FC = C(0). Variable costs are those that vary with output. VC = C(q) - FC

Mathematical Cost Functions - 3 Fixed and Variable Cost MC AVC ATC

Mathematical Cost Functions - 3 Fixed and Variable Cost MC AVC ATC MC cuts ATC and AVC at their minima; minimum of ATC later than min of AVC

Mathematical Cost Functions - 3 Fixed and Variable Cost MC AVC ATC MC cuts ATC and AVC at their minima; minimum of ATC later than min of AVC  AVC  MC

Mathematical Cost Functions - 3 Fixed and Variable Cost MC AVC ATC MC cuts ATC and AVC at their minima; minimum of ATC later than min of AVC  AVC  MC  AVC < ATC

Mathematical Cost Functions - 3 Fixed and Variable Cost MC AVC ATC MC cuts ATC and AVC at their minima; minimum of ATC later than min of AVC  AVC  MC  AVC < ATC  As q , AVC  ATC

Mathematical Cost Functions - 3 One last Problem C = q + 4q 2.

Mathematical Cost Functions - 3 One last Problem C = q + 4q 2. FC = 10 VC = 20q + 4q 2

Mathematical Cost Functions - 3 One last Problem C = q + 4q 2. FC = 10 VC = 20q + 4q 2 AFC = 10/q AVC = q

Mathematical Cost Functions - 3 End ©2003 Charles W. Upton