Jim Whitney Economics 250

Wednesday, March 06, 2013
 

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

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   13.33      
1 4 90 50   22.5      
1 5 150 whitespace.gif (816 bytes)60 whitespace.gif (816 bytes) whitespace.gif (816 bytes)30 whitespace.gif (816 bytes)    
1 6 190 whitespace.gif (816 bytes)40 whitespace.gif (816 bytes) whitespace.gif (816 bytes)31.67 whitespace.gif (816 bytes)    
1 7 210 whitespace.gif (816 bytes)20 whitespace.gif (816 bytes) whitespace.gif (816 bytes)30 whitespace.gif (816 bytes)    
1 8 215 5   26.875      
whitespace.gif (816 bytes)
Resource productivity
(MPL and APL)		 Unit costs
(MC and AVC)