Micro-/Macroeconomics Skills: Equations
Point Elasticity:
Measures the degree of sensitivity of quantity demanded, or quantity supplied to
changes in any determinant
Measures the percentage change in the dependent variable caused by the
percentage change in the independent variable (determinant), holding the values of
other variables constant:
Y
X
X
Y
X X
Y Y
/
/
Arc Elasticity:
Calculates the Average E between points on the Curve:
2 1
2 1
Y Y
X X
X
Y
+
+
(summary measure of all points)
Cross Elasticity (of Demand):
r
x
c
P
QD
=
%
%
Income Elasticity (of Demand):
c
x
y
Y
QD
=
%
%
Price Elasticity (of Demand):
x
x
D
P
QD
p
=
%
%
DP Equation:
!"#
$ C % & % ! % '(
!"# $ Consumption % &nvestment % !overnment #urchases % 'et E)ports
*o say it short:
a) +emember that at equilibrum: $C%&%! (closed economy)
b) ,e -now that .aving is the revenue that is not consumer either by the consumers
(C) or the government (!) so: .$/C/!
c) .o at equilibrium we have: .$& and if we ta-e into account government spending !
and revenue * we have &% ! $ .%* or (!/*) $ (./&)
d) Economic crisis $0 .0& $0 demand is insufficient $0 the state must
counterbalance the difference between . and & by a budget deficit (!0*)
A change in any of the components of autonomous spending (Ca, &, !, 'et
e)ports$'() has a mutliplier effect, i1e1 it generates an increase in the overall
revenue (thin- of the different waves of e)penditures they induce)1 *his increase
depends on the marginal propensity is equal to: 23(2/M#C)$23M#. where M#.
stands for marginal propensity to save1
&n case of an open economy, the multiplier is less than in a closed economy as some
of the additional demand will be satisfied by import which does create waves of
spending in the domestic economy1 *he multiplier will be 23(2/M#C % M#M) where
M#M stands for marginal propensity to import1
d$delta
M$d3d& or d3d! etc
Multi!lier "it# In$estment:
4or a new 5evel of &nvestment &
6
, we have
4or a new level of &nvestment &
2
, we have
.ubstituting for the levels of 7utput, we have
8ecause (&
2
9 &
6
) is the Change in &nvestment, we can write:
o$ernment S!endin%:
Summary:
!overnment E)penditure: 2 3 M#.
*a) Multiplier: /M#C 3 M#.
8alanced 8udget: 2
,ith *rade: 2 3 (2 9 M#C % M#M)
,ith *a) and *rade: 2 3 (2 9 M#C (2 9 t) % M#M)
M#C $ Marginal #ropensity to Consume
M#. $ Marginal #ropensity to .ave
M#M $ Marginal #ropensity to &mport
t $ *a) +ate
&uantity '#eory of Money:
V M P Y = (E)ponential)
V
dV
M
dM
P
dP
Y
dY
+ = +
(!rowth)
Y
dY
($ +eal !rowth, constant (short/term)) %
P
dP
($ &nflation) $
M
dM
($ :ariation of Money .upply) %
V
dV
($ :ariation of :elocitiy, constant (short/
term))
Co(( Dou%las Production )unction:
K AL Y =
$ total output
5 $ labor input
; $ capital input
A $ total factor productivity
Alpha $ output elasticity of A5
8eta $ output elasticity of ;
e1g1, Alpha $ 1<, an increase in 5 by 2= would increase by 1<=
Alpha % 8eta $ 2 (constant returns to scale)
e1g1, (5%26=) % (;%26=) $ (%26=)
A % 8 > 2 (decreasing) A % 8 0 2 (increasing)
*!timal +irin% ,ule:
M+# $ M+C
M+# $ Marginal +evenue #roduct of the variable &nput
(%2 wor-er $ %2 sale)
M+C $ Marginal +esource Cost of the variable &nput
(%2 wor-er $ increase in total costs)
Equimar%inal Princi!le:
y
y
x
x
P
MU
P
MU
=
r
MPK
w
MPL
=
-aria(le Costs:
Costs that are a function of 7utput
)i.ed Costs:
Costs that do not vary directly with 7utput (e1g1 +ents)
'otal Costs:
*C $ *4C % *:C
A$era%e )i.ed Costs:
A4C $ *4C 3 ?
A$era%e -aria(le Costs:
A:C $ *:C 3 ?
A$era%e 'otal Costs:
A*C $ *C 3 ? $ A4C % A:C
