The Multiplier-Accelerator Model

Annick AshleyStephanie Chapman

Mir Inaamullah

The Accelerator Effect

Measures how much the growth of the market economy alters the amount of private fixed investment (i.e. investment in tangible capital goods or the replacement

of depreciated ones). Analyzing the Gross Domestic Product, (GDP)

As it increases businesses will, in theory, see rising profits, higher sales and more cash flow.

Business will then have more confidence in their ability to boost profit; thus they will more likely expend more money on private fixed investment.

The Multiplier Effect

Used more generally to measure how an exogenous variable affects an endogenous one.

Involves how one’s spending essentially becomes another’s income.

Ultimately, there is a much greater impact on the equilibrium of national income.

Aggregate Supply vs. Aggregate Demand

The vertical arrows represent a constant rise in demand

Horizontal arrows represent the resulting shift in supply from the two equilibrium points. Small change in the former creates a much greater difference in the latter.

Once aggregate demand rises expected sales and output increase higher employment rates and income more consumption raising aggregate demand yet again.

Example Company invested 200 million dollars into a new

manufacturing plant. Expenditures.

The businesses supplying capital goods have new income Then they, in theory, will spend around 3/5 of their new profits Other businesses will gain $120 million collectively.

Thus, the total economy has gained $(200 + (3/5) * 200)) million

The producers who gained the $120 million will likewise use 3/5 of their profits

We now have a total amount of $(200 + ((3/5) * 200) + ((3/5) + 120)) of new income in the economy.

The cycle will continue but note that the rise in spending decreases by a fraction each step of the way.

Savings Rate Investment into savings accounts can increase monetary

circulation. Federal Reserve sets the reserve requirement to 20% A bank can loan up to $80 of a 100-dollar customer deposit. The $80 will be, then, deposited into another bank that can

then loan out another $64 It only truly affects circulation when money is deposited

domestically, but it essentially gives the Fed great power to affect money supply.

If the Fed notes a recession in the economy and raises the reserve requirement to somewhere around 40%, much less money would be circulating in this same multiplier effect.

Building the Model set up the model estimate parameter values

v = capital stock ratio s = savings rate

obtain final equation

Analyze the Bifurcation

s = 0.08 s = 0.10 s = 0.30

origin goes from unstable to stablemust be a bifurcation!

super-critical Hopf

Application to Actual Data

check data over last 16 quarters

correlates with big drop

explanation: exogenous shock to the economy

RECESSION

Three-Dimensional Model

Model A

k

rIs

rI

sIvr

rsvr

)sin(

3)1(

3

Model B

k

rIs

rI

sIvr

rsvr

)sin(

3)1(

3

**new parameter k: resistance of the savings rate to change

Conclusions

Multiplier-Accelerator model describes macro-economic trends

The two-dimensional model results in a Hopf bifurcation as the savings rate changes

The three-dimensional model results in periodic movement of the savings rate