"There are three kinds of economics: Greek-letter, up-and-down, and airport." Paul Krugman

Equations to Remember

• Real v. Nominal 
• Present Value
• Aggregate Demand
• National Income Identity
• Keynes Spending Multiplier
• Quantity Theory of Money
• Money Multiplier
• Productivity
• Growth Equation
• Cost-disease of Service Sector

Real v. Nominal 

Describes the relationship between actual (nominal) variables and real (inflation adjusted) variables. 

R = N/PI

Where 

• R = real value
• N = nominal value
• PI = price index (level of prices)

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Present Value Equation 

Describes the relationship between the values at two points in time.  Actually it can be thought of as an equation with four unknowns, and all you need to do is solve for the one unknown.   Below is the equation where future value (FV) is the unknown.  

FV = PV*(1 + g)^T

or

PV = FV/(1 + g)^T

Where:

• PV = Present Value ( value at beginning of the period)
• FV = Future Value ( value at the end of the period)
• g = Average growth rate per period
• T = Number of time periods

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Aggregate Demand 

Describes the components of aggregate demand (AD).

AD = C + I + G + X - M

Where 

• AD = aggregate demand
• C = consumption spending (Cars, education, food...)
• I = investment spending (offices, factories, computers, homes...)
• G = government spending (soldiers, judges, teachers, highways...)
• X = exports 
• M = imports

National Income Identity 

Describes the relationship between aggregate supply (Q) and aggregate demand 

(1) Q = C + I + G + X - M

Aggregate Supply = Aggregate Demand

Where 

• Q = AS = aggregate supply
• AD = C + I + G + X - M
• C = consumption spending (Cars, education, food...)
• I = investment spending (offices, factories, computers, homes...)
• G = government spending (soldiers, judges, teachers, highways...)
• X = exports 
• M = imports

Keynesian spending multiplier

Describes the impact a change in government spending will have on the level of income.  

DY/DG = 1/(1-MPC)

Where 

• DY = change in national income (GDP)
• DG = change in government spending
• MPC = marginal propensity to consume = DC/DY = change in consumptions spending per unit change in income
• An Introduction to Economics

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Quantity Theory of Money

Describes the relationship between money and nominal GDP (PY).

MV = PY

Describes the relationship between the growth rate in money supply and inflation rate.

m + v = p + y

Where:

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Money Multiplier

Describes the relationship between the amount of high-powered money the Fedputs in the system and the eventual increase in the money supply. 

DM/DM_h = 1/(rrr)

Where:

• DM = change in the money supply
• DM_h = change in high-powered money (cash)
• rrr = required reserve rate 
• T = Number of time periods

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Productivity 

Describes the relationship between labor productivity and multifactor productivity.

y = m + b*h + c*k

or

y-h = m + c*(k-h)

Where:

• y = growth rate in output

• m = multifactor productivity

• y-h = growth rate in labor productivity

• h = growth rate of labor 

• k = growth rate of capital (machinery)

• c =  capital's share of total cost 

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Growth decomposition

Decomposes the GDP per person into efficiency (labor productivity) and resources intensity (Labor force participation)

(1) Y/P = (Y/L)*(L/P)

Decomposes the growth in GDP per person into growth generated by increases in efficiency (productivity) and increases in resources.  

(2) (y/p) = (y/l) +(l/p)

Where:

Y = real GDP	y/p = percentage change in real GDP per person
P = population	y/l = percentage change in labor productivity
L = labor force	l/p* = percentage change in labor participation rates

* the ratio of the labor force to the population is very close to, but not quite the same as the labor force participation rate that measures the percentage of the working age population in the labor force.  The first of these measures, the one included in the equation, would be directly affected by the movement of the baby boomers into the market, while the second would not be directly affected. 

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Cost-disease of the service sector

Decomposes the growth in prices into two components - the growth in wages and the growth in productivity

p = w - %D (Q/L)

Where:

• p = percentage change in price
• w = percentage change in wages
• %D(Q/L) = percentage change in labor productivity
• Q = output
• L = labor input

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