Today’s Outline:
•
ShortRun Costs
•
Implications of diminishing marginal returns to labor
•
=
MC
wMPL
•
=
AVC
wAPL
•
Effects of perunit taxes
•
•
Slope of TC is ATC
•
•
Short Run Costs:
•
=
+
TC
FC VC
•
FC are capital costs and VC are labor costs
•
=
=
MC
dTCdq
dVCdq
=
wdLdq
o
Because FC is constant
o
=
FC
rK
and
=
VC
wL
o
As q increases, the firm needs to hire more labor
•
=
MPL
dqdL
•
=
1MPL
dqdL
•
So
=
×
=
MC
w
dLdq
wMPL
•
•
•
At some point, diminishing marginal returns kicks in and L and q move in the
same direction so MC is increasing
•
If
<
dMPLdL 0
, this means we have diminishing marginal returns
•
Some production functions do not have diminishing marginal returns
•
=
=
=
AVC
VCq
wLq
wAPL
o
Use
=
APL
qL
and
=
1APL
Lq
•
Costs are tied to production functions
•
•
Effects of PerUnit Taxes:
•
Perunit taxes can be written tq where t is perunit tax and q is quantity
•
•
Example: Before tax, the cost function is
=
Cq
q2
and after the tax, the function is
+
=
+
Cq tq
q2 tq
. Write the cost function in terms of q.
•
Before tax:
=
MC
2q
•
After tax:
=
+
MC
2q t
•
Since
=
+
TC
FC VC
, then
=
=
MC
dTCdq
dVCdq
since the only component in TC
that is changing is VC
•
Perunit tax shifts MC up by an amount of the perunit tax
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•
•
Long Run: Cost Minimization:
•
Isocosts are like budget constraints
•
Along isocosts, costs are fixed
•
=
+
C
wL rK
•
•
•
Graph isocost by writing equation of K in terms of L
o
Rearrange to
=
+
y
mx b
form
o
=

rK
C wL
o
=

K
Cr wrL
•
Isocost lines are a set of straight parallel downward sloping lines with a slope of

wr
(always linear)
•
Same total cost along an isocost
•
The closer to the origin, the lower the cost
o
o
Cost Minimization:
•
Graphically choosing lowest isocost
•
Finding tangency point (only works with wellbehaved production functions)
•
Bangforthebuck condition/last dollar equivalence
o
o
•
Like in utility, budget constraints, and indifference curves, best way to produce
quantity is lowest cost, which is the tangency point
o
o
•
Choose highest indifference curve
•
Slope of isocost =

wr
•
Slope of isoquant =

=
MPLMPK
MRTS
o
o
At tangency point:
•

=
wr

MPLMPK
•
=
MPLMPK
wr
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 Fall '08
 Betts,J
 Economics, Microeconomics, Economics of production, long run costs, o Slope

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