Econ 102: Principles of Macroeconomics - IS-MP Model Study Notes

Today's discussion focuses on the relationship between output and interest rates.
Future lectures will introduce aggregate prices and culminate in a full model of business cycle fluctuations, including booms, busts, and recoveries.
Ceteris Paribus Assumptions for Today's Discussion:
1. Hold inflation constant: This is based on the "sticky price" assumption.
2. Capacity to produce: Assumes that firms can adjust their production based on demand without price signals.
3. Expected future output: Simplifies the Investment function, particularly the term E(Y(t+1)).

Holding inflation constant simplifies the consumption function and allows focus on the real interest rate, which is pivotal in future discussions regarding the central bank's consideration of inflation.
The assumption of capacity to produce is essential for equilibrium to occur even without price signals; firms adjust production according to demand.
Expected future output helps streamline our analysis, much like transitioning from a short run to a long run perspective.

Definition: AE is the spending plans in an economy over a year, representing the willingness to buy.
Types of Spenders:
- Households
- Firms
- Government
- Foreigners
Mathematical Representation:
- AE = C + I_p + G + NX
- Where ( I_p ) is planned investment, referring specifically to firm purchases of new capital.
Clarification: Plans may differ from actual output. Economists are more interested in OUTPUT (actual production) rather than DESIRED OUTPUT.

Actual Output (Y):
- Defined as GDP: ( Y = C + I + G + NX )
- The key distinction lies in that actual investment (I) accounts for all firm purchases while planned investment (( I_p )) is specifically capital investment.
Relationship Between AE and Y:
- Discrepancies where ( AE
  eq Y ) occur when ( I_p
  eq I ).
- If ( I > I_p ), it indicates an unintended accumulation of inventories since buyers aren't desiring all that producers have made.
- Conversely, if ( I_p > I ), there is a need for increased production as inventories do not meet demand.

If plans diverge from actual output:
- If ( I > I_p ):
- Output (Y) exceeds aggregate expenditure (AE), causing output to drop until equilibrium (Y = AE) is reached.
- If ( I_p > I ):
- Output (Y) falls short of aggregate expenditure (AE), prompting an increase in output to meet rising demand.
Implication: The IS-MP model operates under assumptions that capacity to produce remains fixed, and output adjusts according to demand — supporting Keynesian views that emphasize demand's role in driving the economy.
Equilibrium Point: ( Y = AE ) implies ( I = I_p )—indicating equilibrium where output is determined entirely by demand regardless of production capacity.

Recapping concepts as they relate to the IS curve:
- Definitions:
- Consumption Function: ( C = C(Y, r) )
- Investment Function: ( I = I(r) )
- Government Spending Function: ( G = G(r) )
- Net Exports: ( NX = NX(r) )
Observation: Demand generally increases as the interest rate decreases – known as Interest Sensitivity (IS).
Influences on Interest Sensitivity:
- Investment and Net Exports are most responsive to interest rate changes.
- Government Spending (G) is typically less sensitive as many forms are autonomous and represent a negligible portion of overall fiscal policy.

The IS curve graphically represents aggregate expenditure as a downward-sloping function of the real interest rate, indicating that lower interest rates correspond with higher output (Y).
Significance: The real interest rate is critical for economic choices, as it reflects direct spending across different sectors.
Real vs. Nominal Interest Rate: When inflation is fixed, the real interest rate equals the nominal interest rate, facilitating various spending behaviors in equilibrium.

The Role of the Federal Reserve (Fed):
- Acts as the United States' central bank, managing the money supply and interest rates.
- The Fed has the authority to set the baseline real interest rate, influencing borrowing across the economy.
Mechanics of Monetary Policy:
- By decreasing interest rates, the Fed stimulates borrowing, which increases the money supply leading to consequential impacts on prices and productivity, summarized through the equation: ( MV = PQ ).
Interest Rates as Baseline:
- The Fed sets overnight inter-bank rates, creating a foundation for all lending rates in the economy and effectively functioning as the risk-free interest rate.

Real Interest Rate Components:
- Defined as: ( real ext{ } interest ext{ } rate = risk-free ext{ } interest ext{ } rate + risk ext{ } premium )
- The risk-free rate represents a lender's opportunity cost on short-term loans, whereas the risk premium compensates for market risks associated with longer or riskier investments.
Fisher Equation:
- Relates nominal interest rates to real rates and inflation: ( nominal = risk-free rate + risk premium + inflation ).

MP Curve Equation:
- Expressed as: ( r = 6 ) indicating a set interest rate.
- IS is defined by: ( Y = 20 - rac{3}{4}r ).
Finding Equilibrium:
In equilibrium, set MP equal to IS:
- Solve for Y*:
- ( Y* = 20 - rac{3}{4} imes 6 = 15.5 )
- Hence, when r = 6, ( Y* = 15.5 ).
Intervention Mechanism:
- The Fed may perceive output of Y = 15.5 as too low, thus undertaking expansionary monetary policy to stimulate higher levels of output through reduced interest rates.

Government's Reactions:
- If the government believes Y = 15.5 is suitable, G can shift the IS curve right, increasing equilibrium output.
Multiplier Effect:
- Defines how much GDP varies due to changes in government spending:
- Overall equation: ( ΔGDP = Δspending * multiplier )
Example Calculation of Multiplier:
- If the multiplier is 2.5, implying that each dollar in new government spending yields $2.5 in total economic activity, the necessary increase in G to achieve a desired GDP change can be calculated by:
- ( ΔGDP = $15.5 - $13 = $2.5 )
- Implying ( ΔGDP = ΔG * multiplier )

Designing Fiscal Policy:
- Alignment with the multiplier allows for precise adjustments to fiscal policy based on the desired output levels.
- Future lectures will explore deeper into how the multiplier is derived.