IS-LM Model

Assumptions

• linear consumption function
• closed economy

IS-LM Model

the IS-LM Model is used to model how the GDP changes from one year to another. A short-term model compared to the long-term methods mentioned previously.

$GDP=C+I+G+X-M=C+I+G+NX$

$I$ … Investments (private and companies) $G$ … Government Expenditure $C$ … Consumption (private individuals) $X$ … Exports $M$ … Imports $NX$ … Net Exports

Assuming a closed consumption: $NX=0$

Consumption $C$

a function defined on disposable income: $f(Y^D)=f(Y-T)$ $T$ … Taxes $c_0$ … “substistence” consumption (base consumption) $c_1\in (0,1)$ … (marginal) propensity to consume when income increases

with a linear model we end up with: $C=c_0+c_1\ast Y^D$

$1-c_1$ … investment rate (because one can either spend or save income)

Investments $I$

• interest rate: $i$ Exogenous Number
  • interest rate … cost of borrowing money
  • if borrowing money is more expensive I can borrow less, therefore invest less
• $I=f(Y,i)$
• assumption: linear investment function
  • $d_0+d_1\ast Y-d_2\ast i$

Government Expenditure $G$

• Exogenous Number
• would be dependent on taxes … not in this model tho
• e.g. roads, universities, wages

Putting it all together

$GDP=I+G+c_0-c_1\ast T+c_1\ast Y$

Equilibrium $Z=Y$

aggregate demand = aggregate supply $GDP=Y$ This will be a classic $y=x$ line

Where both lines meet the equilibrium is located

• line 1: $y=x$
• line 2: $Y=Z$

Equilibrium $I=S$

• private saving: $S^P=Y-T-C⟹C+I+G-T-C=I+G-T$
  • income - taxes - consumption
• government saving: $S^G=T-G$
  • taxes - government spending
• $S=S^P+S^G=I-T+G+T-G=I$
• $S=I$

Transformations

$Y^{\ast }=\frac{1}{1-c_1}(I+G+c_0-c_1\ast T)$

more government expenditure → $GDP\ast \frac{1}{1-c_1}$ $\frac{1}{1-c_1}$ … multiplicator, Fiscal Multiplier

more taxes → $GDP\ast \frac{c_1}{1-c_1}$ $\frac{c_1}{1-c_1}$ … fiscal factor for taxes

Paradox of Thrift

• when saving more (decrease $c_0$) the GDP decreases in the short run
• but the savings will finance the long-run development
• Ricardian equivalence theory

Fiscal Multiplier

There are economies where the fiscal multiplier is smaller than 1.