schema: EconSchema
aspectRatio: 1.3
params:
- name: a
value: 0.3
min: 0.3
max: 0.5
round: 0.01
- name: L
value: 50
min: 20
max: 70
round: 0.01
- name: s
value: 0.3
min: 0.1
max: 0.5
round: 0.01
- name: b
value: 0
min: 0
max: 1.5
round: 0.01
- name: m
value: 298.5
min: 298.5
max: 451
round: 0.1
calcs:
Keq: (((calcs.req)/((params.a)((params.L)^(1-params.a))))^(1/(params.a-1)))
req: (((params.a)*(calcs.S)^(params.a-1))(params.L)^(1-params.a))
Yeq: (((calcs.Keq)^(params.a))(params.L)^(1-params.a))
Yeq2: (((calcs.Keq)^(params.a))*(70)^(1-params.a))
K: (((params.a)(24)^(params.a-1))(params.L)^(1-params.a))
S: (((params.s)*(params.L)^(1-params.a))^(1/(1-params.a)))
WLreal: ((1-params.a)((calcs.Keq)^(params.a))((params.L)^(-params.a)))
pi1: ((((calcs.DEMmk))*(calcs.QRMg))-(((calcs.L)*(calcs.WLreal))+((calcs.Keq)*(calcs.req))))
P: (((calcs.WLreal)/((1-params.a)((calcs.Keq)^(params.a))))(((calcs.Yeq)/((calcs.Keq)^(params.a)))^((params.a)/(1-params.a))))
iso: (((calcs.pi1/((calcs.DEMmk)))+((calcs.WLreal)*(80)/((calcs.DEMmk)))+((calcs.req)*(calcs.Keq)/((calcs.DEMmk)))))
of: (((calcs.WLreal)/((1-params.a)((calcs.Keq)^(params.a))))(((65)/((calcs.Keq)^(params.a)))^((params.a)/(1-params.a))))
of2: (((calcs.Keq)^(params.a))(((((1)-(params.a))(calcs.Keq)^(params.a))(1.5))/(calcs.WLreal))^(((1)-(params.a))/(params.a)))
DEMmk: ((calcs.P)-((params.b)/(100))((calcs.QRMg)-(calcs.Yeq)))
#2 expansão de taylor#
QRMg: (((calcs.Yeq)((1)+((((1)-(params.a))(calcs.Yeq)(params.b))/((100)(params.a)(calcs.P)))))/((1)+((((1)-(params.a))(calcs.Yeq)(params.b))/((50)(params.a)(calcs.P)))))
RMg: ((calcs.P) - (((params.b)(calcs.QRMg))/(50)) +(((params.b)(calcs.Yeq))/(100)) )
WLreal2: ((1-params.a)((calcs.Keq)^(params.a))((60)^(-params.a)))
MK: ((calcs.DEMmk)/(calcs.RMg))
L: (((calcs.QRMg)/((calcs.Keq)^(params.a)))^((1)/((1)-(params.a))))
L2: (((((1)-(params.a))((calcs.Keq)^(params.a)))/(2))^((1)/(params.a)))
WLreal3: ((calcs.RMg)(1-params.a)((calcs.Keq)^(params.a))((60)^(-params.a)))
P1: ((298.5)(calcs.V)/(calcs.Yeq))
P2: ((params.m)(calcs.V)/(calcs.Yeq))
P3: ((10)*(calcs.Yeq)(calcs.V)/(calcs.QRMg))
Ym: ((params.m)(calcs.V)/(calcs.P3))
V: (((calcs.QRMg)(calcs.DEMmk))/((calcs.Yeq)(calcs.P)))
layout:
FourGraphsPlusSidebar2:
topLeftGraph:
xAxis:
min: 0
max: 80
ticks: 4
yAxis:
min: 0
max: 60
ticks: 4
objects:
#Função de Produção de Curto-prazo
- Curve:
fn: "((calcs.Keq)^(params.a))*(x)^(1-params.a)"
ind: x
min: 0
max: 100
color: red
strokeWidth: 3.5
samplePoints: 400
#Função de Isolucro
- Curve:
fn: "((calcs.pi1/((calcs.DEMmk)))+((calcs.WLreal)*(x)/((calcs.DEMmk)))+((calcs.req)*(calcs.Keq)/((calcs.DEMmk))))"
ind: x
min: 0
max: params.L +30
color: grey
strokeWidth: 3.5
samplePoints: 300
- Segment:
a: [0,60]
b: [0, 60]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: Y
position: r
fontSize: 11
- Segment:
a: [80,0]
b: [80,0]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: \ L
position: t
fontSize: 11
- Segment:
a: [params.L, 0]
b: [params.L, 0]
color: white
bgcolor: "'#36a854'"
label:
text: params.L.toFixed(1)
position: t
fontSize: 11
- Segment:
a: [calcs.L, 0]
b: [calcs.L, 0]
color: white
bgcolor: "'#36a854'"
label:
text: calcs.L.toFixed(1)
position: t
fontSize: 11
- Segment:
a: [0, calcs.Yeq]
b: [0, calcs.Yeq]
color: white
bgcolor: "'#36a854'"
label:
text: calcs.Yeq.toFixed(2)
position: r
fontSize: 11
- Segment:
a: [0, calcs.QRMg]
b: [0, calcs.QRMg]
color: white
bgcolor: "'#36a854'"
label:
text: calcs.QRMg.toFixed(2)
position: r
fontSize: 11
- Segment:
a: [params.L, calcs.Yeq]
b: [params.L, 0]
color: green
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [calcs.L, calcs.QRMg]
b: [calcs.L, 0]
show: (params.b>0)
color: green
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [params.L, calcs.Yeq]
b: [0, calcs.Yeq]
color: green
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [calcs.L, calcs.QRMg]
b: [0, calcs.QRMg]
show: (params.b>0)
color: green
lineStyle: dotted
strokeWidth: 2
- Point:
coordinates: [params.L, calcs.Yeq]
color: black
r: 5
- Point:
coordinates: [calcs.L, calcs.QRMg]
color: black
r: 5
- Segment:
a: [70, calcs.Yeq2]
b: [70, calcs.Yeq2]
color: white
bgcolor: "'#d62728'"
label:
text: F(K,L)
position: l
fontSize: 10
- Segment:
a: [50, calcs.iso]
b: [50, calcs.iso]
color: white
bgcolor: grey
label:
text: "`\\\\frac{\\\\pi}{P} + \\\\frac{w_{L}\\\\cdot L}{P} + \\\\frac{w_{K}\\\\cdot K}{P}`"
position: bl
fontSize: 11
bottomLeftGraph:
xAxis:
min: 0
max: 80
ticks: 4
yAxis:
min: 0
max: 1.3
ticks: 4
objects:
#Função de Demanda de Trabalho
- Curve:
fn: "(1-params.a)((calcs.Keq)^(params.a))((x)^(-params.a))"
ind: x
min: 0
max: 100
color: blue
strokeWidth: 3.5
samplePoints: 300
#Função de Demanda de Trabalho2
- Curve:
fn: "(calcs.RMg)(1-params.a)((calcs.Keq)^(params.a))((x)^(-params.a))"
ind: x
min: 0
max: 100
color: blue
lineStyle: dashed
strokeWidth: 3
samplePoints: 300
#Função de Oferta de Trabalho
- Segment:
a: [params.L, 10]
b: [params.L, calcs.WLreal]
color: red
strokeWidth: 3.5
- Segment:
a: [params.L, calcs.WLreal]
b: [0, calcs.WLreal]
color: red
strokeWidth: 3.5
- Segment:
a: [80,0]
b: [80,0]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: \ L
position: t
fontSize: 11
- Segment:
a: [0 ,1.3]
b: [0 ,1.3]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: w_{L}
position: r
fontSize: 14
- Segment:
a: [params.L , 0]
b: [params.L, 0]
color: white
bgcolor: "'#36a854'"
label:
text: params.L.toFixed(1)
position: t
fontSize: 11
- Segment:
a: [calcs.L , 0]
b: [calcs.L, 0]
color: white
bgcolor: "'#36a854'"
label:
text: calcs.L.toFixed(1)
position: t
fontSize: 11
- Segment:
a: [0, calcs.WLreal]
b: [0, calcs.WLreal]
color: white
bgcolor: "'#36a854'"
label:
text: calcs.WLreal.toFixed(2)
position: r
fontSize: 11
- Segment:
a: [calcs.L, 10]
b: [calcs.L, 0]
color: green
show: (params.b>0)
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [params.L, calcs.WLreal]
b: [params.L, 0]
color: green
lineStyle: dotted
strokeWidth: 2
- Point:
coordinates: [params.L, calcs.WLreal]
color: black
r: 5
- Point:
coordinates: [calcs.L, calcs.WLreal]
color: black
r: 5
- Segment:
a: [60, calcs.WLreal2]
b: [60, calcs.WLreal2]
color: white
bgcolor: "'#1f77b4'"
label:
text: w_{L}(L)
position: bl
fontSize: 10
- Segment:
a: [60, calcs.WLreal3-0.2]
b: [60, calcs.WLreal3-0.2]
show: (params.b>0)
color: white
bgcolor: "'#1f77b4'"
label:
text: w_{L}'(L)
position: bl
fontSize: 10
- Segment:
a: [60, calcs.WLreal3-0.2]
b: [60, calcs.WLreal3-0.2]
show: (params.b>0)
color: white
bgcolor: "'#1f77b4'"
label:
text: w_{L}'(L)
position: bl
fontSize: 10
- Segment:
a: [params.L, 1]
b: [params.L, 1]
color: "'#d62728'"
bgcolor: white
label:
text: L
topRightGraph:
xAxis:
min: 0
max: 60
ticks: 4
yAxis:
min: 0
max: 40
ticks: 6
objects:
- Curve:
fn: "(((params.m)(calcs.V))/(x))"
ind: x
min: 0
lineStyle: dashed
show: (calcs.Yeq>calcs.QRMg)
max: 60
label: {text: "`\\\\frac{M \\\\cdot V}{Y}`", x: 50, fontSize: 8}
color: blue
strokeWidth: 3.5
samplePoints: 300
- Curve:
fn: "(((params.m)(calcs.V))/(x))"
ind: x
min: 0
lineStyle: dashed
show: (params.m>=calcs.QRMg) || (params.b>0)
max: 60
label: {text: "`\\\\frac{M \\\\cdot V}{Y}`", x: 50, fontSize: 8}
color: blue
strokeWidth: 3.5
samplePoints: 300
- Curve:
fn: "(((10*calcs.Yeq)(calcs.V))/(x))"
ind: x
min: 0
max: 60
lineStyle: solid
label: {text: "`\\\\frac{M \\\\cdot V}{Y}`", x: 50, fontSize: 8}
color: blue
strokeWidth: 3.5
samplePoints: 300
- Segment:
a: [calcs.Yeq, 0]
b: [calcs.Yeq, 40]
color: red
show: (calcs.Yeq==calcs.QRMg)
strokeWidth: 3.5
- Segment:
a: [calcs.Yeq, calcs.P3]
b: [calcs.Yeq, 40]
color: red
show: (calcs.Yeq>calcs.QRMg)
strokeWidth: 3.5
- Segment:
a: [calcs.Yeq, 30]
b: [calcs.Yeq, 30]
color: red
bgcolor: white
strokeWidth: 1
label:
text: \ Y_{pot}
fontSize: 11
- Point:
coordinates: [calcs.Yeq, calcs.P2]
color: black
show: (calcs.Yeq>=!calcs.QRMg) & (calcs.Yeq < calcs.Ym)
r: 5
- Point:
coordinates: [calcs.QRMg, calcs.P3]
color: black
r: 5
- Point:
coordinates: [calcs.Ym, calcs.P3]
color: black
show: (calcs.Yeq>calcs.QRMg) & (calcs.Yeq>calcs.Ym)
r: 5
- Segment:
a: [calcs.Ym,calcs.P3]
b: [calcs.Ym,0]
color: green
show: (calcs.Yeq>calcs.QRMg) & (calcs.Yeq>calcs.Ym)
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [calcs.Yeq,0]
b: [calcs.Yeq,calcs.P3]
color: green
show: (calcs.Yeq!=calcs.QRMg) & (calcs.Ym>calcs.Yeq)
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [calcs.Yeq,calcs.P2]
b: [0,calcs.P2]
show: (calcs.Yeq>calcs.QRMg) & (calcs.Yeq< calcs.Ym)
color: green
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [0,calcs.P2]
b: [calcs.Yeq,calcs.P2]
color: green
show: (calcs.Yeq==calcs.QRMg)
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [0,calcs.P1]
b: [calcs.Yeq,calcs.P1]
show: (params.m>298.5) & (params.b==0)
color: green
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [calcs.QRMg,calcs.P3]
b: [calcs.QRMg,0]
show: (calcs.Yeq>calcs.QRMg)
color: green
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [calcs.Yeq, 0]
b: [calcs.Yeq, 0]
color: white
show: (calcs.Yeq==calcs.QRMg)
bgcolor: "'#36a854'"
strokeWidth: 1
label:
text: calcs.Yeq.toFixed(2)
position: t
fontSize: 11
- Segment:
a: [0, calcs.P1]
b: [0, calcs.P1]
color: white
show: (calcs.Yeq==calcs.QRMg)
bgcolor: "'#36a854'"
strokeWidth: 1
label:
text: calcs.P1.toFixed(2)
position: r
fontSize: 11
- Segment:
a: [0, calcs.P2]
b: [0, calcs.P2]
color: white
show: (calcs.Yeq==calcs.QRMg)
bgcolor: "'#36a854'"
strokeWidth: 1
label:
text: calcs.P2.toFixed(2)
position: r
fontSize: 11
- Segment:
a: [0, calcs.P3]
b: [0, calcs.P3]
color: white
show: (calcs.Yeq>calcs.QRMg)
bgcolor: orange
strokeWidth: 1
label:
text: calcs.P3.toFixed(2)
position: r
fontSize: 11
- Segment:
a: [0, calcs.P2]
b: [0, calcs.P2]
color: white
show: (calcs.Yeq>calcs.QRMg) & (calcs.Yeq< calcs.Ym)
bgcolor: "'#36a854'"
strokeWidth: 1
label:
text: calcs.P2.toFixed(2)
position: r
fontSize: 11
- Segment:
a: [calcs.QRMg, 0]
b: [calcs.QRMg, 0]
color: white
show: (calcs.Yeq>calcs.QRMg)
bgcolor: orange
strokeWidth: 1
label:
text: calcs.QRMg.toFixed(2)
position: t
fontSize: 11
- Segment:
a: [calcs.Ym, 0]
b: [calcs.Ym, 0]
color: white
show: (params.m>298.5) & (calcs.Yeq> calcs.Ym)
bgcolor: "'#36a854'"
strokeWidth: 1
label:
text: calcs.Ym.toFixed(2)
position: t
fontSize: 11
- Segment:
a: [calcs.Yeq, 0]
b: [calcs.Yeq, 0]
color: white
show: (calcs.Yeq>calcs.QRMg) & (calcs.Yeq< calcs.Ym)
bgcolor: "'#36a854'"
strokeWidth: 1
label:
text: calcs.Yeq.toFixed(2)
position: t
fontSize: 11
- Segment:
a: [calcs.Yeq,calcs.P3]
b: [0,calcs.P3]
show: (calcs.Yeq>calcs.QRMg)
color: red
lineStyle: solid
strokeWidth: 3
- Segment:
a: [1, 40]
b: [1,40]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: \ P_{nível}
position: r
fontSize: 11
- Segment:
a: [60,0]
b: [60,0]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: \ Y
position: t
fontSize: 11
bottomRightGraph:
xAxis:
min: 0
max: 60
ticks: 4
yAxis:
min: 0
max: 1.5
ticks: 6
objects:
#Função de CMg
- Curve:
fn: "(((calcs.WLreal)/((1-params.a)((calcs.Keq)^(params.a))))(((x)/((calcs.Keq)^(params.a)))^((params.a)/(1-params.a))))"
ind: x
min: 0
max: 60
color: red
strokeWidth: 3.5
samplePoints: 300
#Demanda
- Curve:
fn: "(calcs.P)-((params.b)/(100))((x)-(calcs.Yeq))"
ind: x
min: 0
max: 60
label: {text: "`P_{D}(Y)`", x: 53, fontSize: 8}
color: blue
strokeWidth: 3.5
samplePoints: 300
# RMG
- Curve:
fn: "((calcs.P) - (((params.b)(x))/(50)) +(((params.b)(calcs.Yeq))/(100)) )"
ind: x
min: 0
max: 60
show: (params.b)>0
label: {text: "`RMg(Y)`", x: 40, fontSize: 8}
color: blue
lineStyle: dashed
strokeWidth: 3
samplePoints: 300
- Area:
fn1: "(calcs.P)-((params.b)/(100))((x)-(calcs.Yeq))"
fn2: "(((calcs.WLreal)/((1-params.a)((calcs.Keq)^(params.a))))(((x)/((calcs.Keq)^(params.a)))^((params.a)/(1-params.a))))"
fill: grey
opacity: 0.8
min: calcs.QRMg
max: calcs.Yeq
- Area:
fn1: "(calcs.DEMmk)"
fn2: "(calcs.RMg)"
fill: supply
show: (params.b>0)
opacity: 0.4
min: 0
max: calcs.QRMg
- Label:
coordinates: [((calcs.QRMg + calcs.Yeq)/2),(calcs.DEMmk+calcs.RMg)/2]
text: DWL
bgcolor: grey
color: white
fontSize: 7
show: (params.b>0)
- Segment:
a: [calcs.QRMg,calcs.DEMmk]
b: [0,calcs.DEMmk]
show: (params.b>0)
color: supply
lineStyle: solid
strokeWidth: 3
- Segment:
a: [calcs.QRMg,calcs.RMg]
b: [0,calcs.RMg]
show: (params.b>0)
color: green
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [calcs.QRMg,calcs.DEMmk]
b: [calcs.QRMg,0]
show: (params.b>0)
color: green
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [calcs.Yeq,0]
b: [calcs.Yeq,calcs.P]
color: green
lineStyle: dotted
strokeWidth: 2
- Segment:
a: [calcs.Yeq, 0]
b: [calcs.Yeq, 0]
color: White
bgcolor: "'#36a854'"
strokeWidth: 1
label:
text: calcs.Yeq.toFixed(2)
position: t
fontSize: 11
- Segment:
a: [calcs.QRMg, 0]
b: [calcs.QRMg, 0]
color: white
bgcolor: orange
show: (params.b>0)
strokeWidth: 1
label:
text: calcs.QRMg.toFixed(2)
position: t
fontSize: 11
- Segment:
a: [60 ,calcs.of]
b: [60 ,calcs.of]
color: white
bgcolor: "'#d62728'"
strokeWidth: 1
label:
text: P_{Of}(Y)
position: r
fontSize: 11
- Segment:
a: [calcs.of2 ,1.5]
b: [calcs.of2 ,1.5]
color: white
show: (calcs.of>==1.5)
bgcolor: "'#d62728'"
strokeWidth: 1
label:
text: P_{Of}(Y)
position: r
fontSize: 11
- Segment:
a: [0, calcs.DEMmk]
b: [0, calcs.DEMmk]
color: white
bgcolor: orange
strokeWidth: 1
label:
text: calcs.DEMmk.toFixed(2)
position: r
fontSize: 11
- Segment:
a: [0, calcs.RMg]
b: [0, calcs.RMg]
color: white
bgcolor: "'#36a854'"
strokeWidth: 1
label:
text: calcs.RMg.toFixed(2)
position: r
fontSize: 11
- Segment:
a: [60,0]
b: [60,0]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: \ Y
position: t
fontSize: 11
- Segment:
a: [1, 1.5]
b: [1, 1.5]
color: Black
bgcolor: white
strokeWidth: 1
label:
text: \ P
position: r
fontSize: 11
- Point:
coordinates: [calcs.Yeq, calcs.P]
color: black
r: 5
- Point:
coordinates: [calcs.QRMg, calcs.RMg]
color: black
r: 5
- Point:
coordinates: [calcs.QRMg, calcs.DEMmk]
color: black
r: 5
- Segment:
a: [1,calcs.RMg]
b: [1,calcs.DEMmk]
color: blue
bgcolor: none
show:
strokeWidth: 3
endArrow: true
label:
text: MarkUp
position: l
fontSize: 8
sidebar:
controls:
- title: Modelo de Equilíbrio Geral de Competição Perfeita e Imperfeita
sliders:
- param: b
label: b
digits: 3
- param: m
label: M_{of}
digits: 4
divs:
- html:
- html: 'Os resultados relevantes da ${\bf{economia \\\ nominal}}$ são:'
- html: '`$$M_{of}=${params.m.toFixed(1)}$$ $$V=${calcs.V.toFixed(2)}$$ $$P_{nível}= ${calcs.P2.toFixed(2)}$$`'
show: (params.b==0)
- html: '`$$M_{of}=${params.m.toFixed(1)}$$ $$V=${calcs.V.toFixed(2)}$$ $$P_{nível}= ${calcs.P3.toFixed(2)}$$`'
show: ((params.b>0) & (params.m==298.5))
- html: '`$$M_{of}=${params.m.toFixed(1)}$$ $$V=${calcs.V.toFixed(2)}$$ $$P_{nível}= ${calcs.P3.toFixed(2)}$$`'
show: ((params.b>0) & (params.m>298.5)) & (calcs.Yeq > calcs.Ym)
- html: '`$$M_{of}=${params.m.toFixed(1)}$$ $$V=${calcs.V.toFixed(2)}$$ $$P_{nível}= ${calcs.P2.toFixed(2)}$$`'
show: ((params.b>0) & (params.m>298.5)) & (calcs.Yeq <= calcs.Ym)
- html:
- html: 'Os resultados relevantes da ${\bf{economia \\\ real}}$ são:'
- html: '`$$\\pi = ${calcs.pi1.toFixed(2)}$$ $$ Y_{eq}=${calcs.QRMg.toFixed(2)}$$ $$K_{eq}=${calcs.Keq.toFixed(2)}$$ $$ P=${calcs.DEMmk.toFixed(2)} $$ $$ w_{L}= ${calcs.WLreal.toFixed(3)} $$ $$ w_{k}=${calcs.req.toFixed(2)} $$ $$MarkUp= ${calcs.MK.toFixed(2)}$$`'
- html:
- html: Determinação da Oferta
- html: 'A Função de Produção é do tipo Cobb-Douglas : $${F(K,L) = K^a \cdot L^{1-a}}$$'
- html: 'A função de demanda por Capital (K) é dada pela derivada parcial de ${F(K,L)}$ em relação à $K$: $${\frac{\partial F(K,L)}{\partial K}=a \cdot K^{a-1} \cdot L^{1-a}=w_{K}}$$ em que ${\bf{w_K}}$ é a remuneração do Capital (K). De modo que, $${w_{k}= (1+r)}$$ Logo, $${r= w_{k} - 1}$$'
- html: 'A função de oferta de Capital (K) — ou poupança (S) — é modelada como sendo uma proporção constante da renda (Y), dado pelo parâmetro (${s}$): $${S(Y)=s \cdot Y}$$ $${\Longleftrightarrow}$$ $${S(Y) = s \cdot (K^a \cdot L^{1-a})}$$ Resolvendo implicitamente, encontramos: $${s \cdot (K^a \cdot L^{1-a})=K}$$ $${\Longleftrightarrow}$$ $${\frac{K}{K^a}=s \cdot L^{1-a}}$$ $${\Longleftrightarrow}$$ $${K=\left( s \cdot L^{1-a} \right)^{\frac{1}{1-a}}}$$'
- html: 'A função de demanda por Trabalho (L) é dada pela derivada parcial de ${F(K,L)}$ em relação à $L$: $${\frac{\partial F(K,L)}{\partial L}=(1-a) \cdot K^{a} \cdot L^{-a}=w_{L}}$$ em que ${\bf{w_L}}$ é a remuneração do Trabalho (L).'
- html: 'A função de oferta de Trabalho (L) é determinada de maneira exógena e independente da remuneração $w_{L}$.'
- html: '` $$L =${params.L}$$`'
- html: 'A curva de Oferta — ou Custo Marginal (CMg) — dessa economia é obtida a partir da função de de Custo Total (CT): $$CT(Y) = w_{K} \cdot K + w_{L} \cdot L$$ Como estamos no curto-prazo, então o Capital (K) é fixo $$CT(Y) = w_{K} \cdot \bar{K} + w_{L} \cdot L$$ Resolvendo a Função de Produção para L e substituindo, $$CT(Y) = w_{K} \cdot \bar{K} + w_{L} \cdot L(Y) $$ Derivando em relação à Y $$\frac{d CT(Y)}{dY} = w_{L} \cdot L´(Y) dY$$'
- html: '
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- html: Determinação da Demanda
- html: 'A função de Demanda inversa dessa economia é dada por: $$P_{D}(Y)=P^* -\frac{b}{100} (Y - Y^*)$$ em que "$P^*$" é o preço de Competição Perfeita, "$Y^*$" é a quantidade de Competição Perfeita e "$b$" é o coeficiente angular da função de demanda. '
- html: 'Quando $$b=0$$ então a economia está numa estrutura de mercado de Competição Perfeita. Se $b$>0, então é possível estabelecer um $MarkUp$ sobre o Custo Marginal (CMg).'
- html: '
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- html: Determinação do Lado Nominal
- html: 'O lado nominal da economia é determinado pela equação trocas da Teoria Quantitativa da Moeda (TQM), em que: $$M \cdot V = P \cdot Y$$ Resolvendo para o nível de Preços (P), temos $$P_{nível}=\frac{M \cdot V}{Y}$$ Assumindo que o coeficiente de velocidade (V) de circulação é constante e determinado pelo lado real da economia, $$P_{nível}(Y)=\frac{M \cdot \overline{V}}{Y}$$'