Utilisateur:MDCCCC/Notes

PD_t = patrimoine disponible au temps t

$\gamma {\text{ = taux de thesaurisation}}$

$\rho {\text{ = taux de l'epargne productive (s - gamma) }}$

$\tau _{C},\tau _{\mathrm {P} }{\text{ = taux de l'epargne improductive qui rentre dans le circuit}}$

$\delta {\text{ = taux de l'epargne productive consommee}}$

$PD_{0}=Y_{0}=cY_{0}+\gamma Y_{0}+\rho Y_{0}$

$PD_{1}=C_{1}+S_{1}=cY_{1}+\gamma Y_{1}+\rho Y_{1}+(\gamma \cdot \tau _{C})Y_{0}+\rho \cdot \delta (1+r)Y_{0}+(\gamma \cdot \tau _{\mathrm {P} })Y_{0}+\rho (1-\delta )(1+r)Y_{0}+\gamma Y_{0}(\gamma -\tau _{C}-\tau _{\mathrm {P} })$

$PD_{2}=C_{2}+S_{2}=cY_{2}+\gamma Y_{2}+\rho Y_{2}+(\gamma \cdot \tau _{C})Y_{1}+\rho \cdot \delta (1+r)Y_{1}+(\gamma \cdot \tau _{\mathrm {P} })Y_{1}+\rho (1-\delta )(1+r)Y_{1}+$ $\gamma Y_{1}(\gamma -\tau _{C}-\tau _{\mathrm {P} })+\delta (\gamma \cdot \tau _{\mathrm {P} })(1+r)Y_{0}+\delta \cdot \rho (1-\delta )(1+r)Y_{0}+(1-\delta )(\gamma \cdot \tau _{\mathrm {P} })(1+r)Y_{0}+$ $\rho (1-\delta )^{2}(1+r)Y_{0}+\tau _{C}\cdot \gamma Y_{0}(\gamma -\tau _{C}-\tau _{\mathrm {P} })+\tau _{\mathrm {P} }\cdot \gamma Y_{0}(\gamma -\tau _{C}-\tau _{\mathrm {P} })+\gamma Y_{0}(\gamma -\tau _{C}-\tau _{\mathrm {P} })^{2}$

Général : $PD_{t}=cY_{t}+\tau _{C}\gamma \sum _{k=0}^{t-1}Y_{k}(\gamma -\tau _{C}-\tau _{\mathrm {P} })+\sum _{k=0}^{t}[Y_{k}(\gamma (\gamma -\tau _{C}-\tau _{\mathrm {P} })^{t-k}\tau _{\mathrm {P} }+\rho )\sum _{i=0}^{t-k}[((1-\delta )(1+r))^{i}+{\sum _{j=0}^{i-1}\delta (1-\delta )^{j}(1+r)^{j+1}]]}+\sum _{k=0}^{t}Y_{k}(\gamma (\gamma -\tau _{C}-\tau _{\mathrm {P} })^{t-k}$ $PD_{t}=cY_{t}+\sum _{k=0}^{t}[Y_{k}\sum _{i=0}^{t-k}[((1-\delta )(1+r))^{i}+{\sum _{j=0}^{i-1}\delta (1-\delta )^{j}(1+r)^{j+1}]]}$ Say

$PD_{t}=\sum _{k=0}^{t}Y_{k}$ Keynes

$PD_{t}^{\text{say}}-PD_{t}^{\text{keynes}}=cY_{t}+\sum _{k=0}^{t}Y_{k}[\sum _{i=0}^{t-k}[((1-\delta )(1+r))^{i}+{\sum _{j=0}^{i-1}\delta (1-\delta )^{j}(1+r)^{j+1}]-1]}$

Général modifier

$Y=C+S$

$Y=C+G+I+(X-M)$
$Y={\Sigma VA}+TVA+recettes\ douanieres-subventions$
$Y=(w+EBE+r+VA+\Delta stocks)+(T-G+CCF)$

$(S-I)=(Y-M)-(T-G)$

$e_{x/y}={{\Delta x \over x} \over {\Delta y \over y}}$

$Y=Y_{1}+(Y_{1}-C_{1})\times r+Y_{2}\Longleftrightarrow C_{2}=(Y_{1}-C_{1})\times (1+r)+Y_{2}$

Setterfield et Cornwall modifier

$\lambda =\lambda _{0}+\lambda _{g}g$

$g=\gamma _{0}+\gamma _{\lambda }\lambda$

$g=\gamma _{0}+\gamma _{\pi }\pi$

$\pi =\pi _{0}+\pi _{\lambda }\lambda$

$g=\gamma _{0}+\gamma _{\pi }\pi _{0}+(\gamma _{\pi }\pi _{\lambda })\lambda$

$g=\gamma _{0}+\gamma _{\lambda }\lambda +\gamma _{\omega }(\omega -\lambda )$

lambda = taux de croissance de la productivité

gamma = variation du taux de marge

g = croissance économique

pi = profits (part des profits???)

omega = taux de croissance du salaire réel

les "_" signifient "tirés par"

J.B. Say modifier

$O=D$

Keynes modifier

$P_{m}C={\Delta C \over \Delta Y}\qquad PMC={C \over Y}\qquad P_{m}S={\Delta S \over \Delta Y}\qquad PMS={S \over Y}$

$C=c\times Y+C_{0},$ $c\in ]0;1[$

Marx modifier

${Pl \over V}\qquad {Pl \over C+V}\qquad {C \over V}$

${{Pl \over V} \over {C \over V}+1}$

Gossen modifier

${d \over dx}U_{m}<0$

$y=-{P_{x} \over P_{y}}x+{R \over P_{y}}$

${U_{m:x} \over P_{x}}={U_{m:y} \over P_{y}}$

$K=-{p_{L} \over p_{K}}L+{B \over p_{K}}$

Cobb-Douglass modifier

$Y=F(K,L)=K^{\alpha }\times L^{1-\alpha },$ $\alpha \in ]0;1[$

Piketty modifier

$\alpha =r\times \beta$

$\beta ={s \over g}$

$b_{y}=\mu \times m\times \beta$

Philip Wicksteed modifier

$C=w\times h+R\Longleftrightarrow w\times (L_{0}-L)+R\Longleftrightarrow C+w\times L=w\times L_{0}+R$

Bowley modifier

${L \over VA}={2 \over 3};{K \over VA}={1 \over 3}$

Jean Fourastié modifier

${\Delta E \over E}={\Delta Y \over Y}-{\Delta Y_{L} \over Y_{L}}$

Knut Wicksell modifier

${\Delta P \over P}={\Delta w \over w}-{\Delta Y_{L} \over Y_{L}}$

(en étant funky on peut regrouper les 2 formules : ${\Delta E \over E}={\Delta Y \over Y}+{\Delta P \over P}-{\Delta w \over w}$ ).

Milton Friedman modifier

${C_{t}^{P}}=k\times {Y_{t}^{P}}$

Daniel Cohen modifier

$D={\text{dette}}$

${\Delta D \over Y}\ \neq \ {r\cdot D_{t-1}-SBP_{t} \over Y}$ ; mais : $\underbrace {\Delta D \over Y} _{\text{déficit public en pourcent du PIB}}\ =\ \underbrace {r\cdot D_{t-1}-SBP_{t} \over Y} _{\text{calcul déficit sans correction }}\ -\ \underbrace {p_{t}\cdot {D_{t-1} \over Y}} _{\text{taxe inflationiste}}-g_{\text{réel}}$