This class exercise is from W8 in MT and covers Profit Maximisation and Cost Minimisation (Production Theory topic). All the exercises are thoroughly calculated, clearly written with good explanation and accurate solutions.
Firms want to find the optimal inputs ( i. ✗F)
✗ to maximize output y* .
Firms
goal :
cost minimization
profit maximization
1. find y at
g- 1 .
find × ? ( Ia vi. a. wa)
,
and fix ×a=×I
✗ it satisfies the point where the
slope of profit
Iso
2.
find × ? ( if ,
W
, , wz ) by equating is
equal the
slope of production function f- (a)
×É(y ,
w
, , wa ) MPa =
¥
the isocost and
slope of an
the
slope of an
isoquant 2 .
find optimal XI
c(✗Y XY) ( Ia) into IT
, plug ✗ profit function
3.
plug (✗Y XY ) into
,
the cost function take FOC of it to
find ×, that maximizes IT
to get alg)
4.
plug e(y ) into F-
py
-
dy )
and find optimal y
✗
Ln
•
Iso
quant
•
' so cost
←
> 4
✗
Ln
-
an
Optimazing firm wanting to produce g-
I
:::÷i:
{ iii.
will choose 4-
at this point we waste our resources
4=5×2 =
✗
=
4-
E-
=
%
.
y=y-
i
at this point we dont achieve
y
=
4-
, TC wa
TC =
X, W +
Xawz ATC = =
w + I
,
g- ,
*
for labour and
capital :
ATC is a constant measure whereas
,
TC = L .
W + Kar w
wage
-
,
rent constant it
r TC not linear function
-
is is a
,
of output
so TC =
g- w
,
+ ¥ wa =
c
(g)
how much
optimisation behavior will tell
you
(at minimum ) it will cost
you
to produce 4-
as we found the
optimal it and ✗I
✗
ntcly) at DRS
NATC (y )
at CRS at DRS
at CRS
WRS
we assume 1--6=0
> 4
at IRS
> 4
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