Jim Whitney Economics 250

Wednesday, March 06, 2013
 

Costs in the short run: The relationship between resource productivity and production costs: KEY

Key formulas:
(1) MC = PL/MPL. Note that MC rises only with diminishing MPL.
(Proof: MC = DTC/DQ = DTVC/DQ = D(PL.L)/DQ
        = PL.(DL)/DQ = PL / (DQ/DL) = PL/MPL)
(2) AVC = PL/APL. Note that AVC rises only with diminishing APL.
(Proof:  AVC = TVC/Q = PLL/Q = PL/(Q/L) = PL/APL)
   
Example: The costs of producing DVDs.
Suppose PL = $60; PK = $360.
   
Complete the following table and the diagrams below it:
K L Q MPL MC=PL/MPL APL AVC=PL/APL AFC ATC
1 1 4 4 $15.00 4 $15.00 $90.00 $105.00
1 2 16 12 $5.00 8 $7.50 $22.50 $30.00
1 3 40 24 $2.50 13.33 4.50 9.00 13.50
1 4 90 50 $1.20 22.5 2.67 4.00 6.67
1 5 150 whitespace.gif (816 bytes)60 whitespace.gif (816 bytes)$1.00 whitespace.gif (816 bytes)30 whitespace.gif (816 bytes)2.00 2.40 4.40
1 6 190 whitespace.gif (816 bytes)40 whitespace.gif (816 bytes)$1.50 whitespace.gif (816 bytes)31.67 whitespace.gif (816 bytes)1.89 1.89 3.78
1 7 210 whitespace.gif (816 bytes)20 whitespace.gif (816 bytes)$3.00 whitespace.gif (816 bytes)30 whitespace.gif (816 bytes)2.00 1.71 3.71
1 8 215 5 $12.00 26.875 2.23 1.67 3.91
whitespace.gif (816 bytes)
Resource productivity
(MPL and APL)		 Unit costs
(MC and AVC)