## Economics Formulas

• The demand function captures the effect of all these factors on demand for a good.
Demand function: $QD_x = f(P_x, I, P_y, ...)$ … (Equation 1)
Equation 1 is read as "the quantity demanded of Good X (QDX) depends on the price of
Good X (PX), consumers' incomes (I) and the price of Good Y (PY), etc."

• The supply function can be expressed as:
Supply function: $QS_x = f(P_x, W, ...)$ 

• The own-price elasticity of demand is calculated as:
$ED_{P_x} = {%ΔQD_x} / {% ΔP_x}$
If we express the percentage change in X as the change in X divided by the value of X,
the equation can be expanded to the following form: $ED_{P_x} = { % ΔQD_x} / {% ΔP_x} = {{ΔQD_x} ⁄ {ΔQD_x}} / {{ΔP_x} ⁄ P_x} = ({ΔQD_x} / {ΔP_x}) (P_x/{QD_x})$

• $E_p = {\text"% change in quantity demanded"} / {\text"% change in price"}$
$= { % ΔQ_d} / {% ΔP}$
$= {(Q_0 - Q1) / {(Q_0 + Q_1)\/2} × 100} / {P_0 - P1) / {(P_0 + P_1)\/2} × 100}$

• Income elasticity of demand measures the responsiveness of demand for a particular good to a change in income, holding all other things constant.
$ED_1 = { % ΔQD_x} / {% ΔI} = {{ΔQD_x} ⁄ {QD_x}} / {ΔI/I} = ({ΔQD_x} / {ΔI}) (I/{QD_x})$
$E_I = {\text"% change in quantity demanded"} / {\text"% change in income"}$ $•$ $Cross elasticity of demand measures the responsiveness of demand for a particular good to a change in price of another good, holding all other things constant.$ED_{P_y} = { % ΔQD_x} / {% ΔP_y} = {{ΔQD_x} ⁄ {QD_x}} / {{ΔP_y} ⁄ P_y} = ({ΔQD_x} / {ΔP_y}) (P_Y/{QD_x})E_C = {\text"% change in quantity demanded"} / {\text"%change in price of substitute or complement"} $•$ $In general a utility function can be represented as:$U = f(Q_{x_1}, Q_{x_2}, ..., Q_{x_n}) $•$ $Accounting profit (loss) = Total revenue – Total accounting costs.$ $•$ $Economic profit (also known as abnormal profit or supernormal profit) is calculated as: Economic profit = Total revenue – Total economic costs Economic profit = Total revenue – (Explicit costs + Implicit costs) Economic profit = Accounting profit – Total implicit opportunity costs$ $•$ $Normal profit = Accounting profit - Economic profit$ $•$ $Revenue Calculation Total revenue (TR) Price times quantity (P × Q), or the sum of individual units sold times their respective prices; ∑(Pi × Qi) Average revenue (AR) Total revenue divided by quantity; (TR / Q) Marginal revenue (MR) Change in total revenue divided by change in quantity; (ΔTR / ΔQ)$ $•$ $Costs Calculation Total fixed cost (TFC) Sum of all fixed expenses; here defined to include all opportunity costs Total variable cost (TVC) Sum of all variable expenses, or per unit variable cost times quantity; (per unit VC × Q) Total costs (TC) Total fixed cost plus total variable cost; (TFC + TVC) Average fixed cost (AFC ) Total fixed cost divided by quantity; (TFC / Q) Average variable cost (AVC) Total variable cost divided by quantity; (TVC / Q) Average total cost (ATC) Total cost divided by quantity; (TC / Q) or (AFC + AVC) Marginal cost (MC) Change in total cost divided by change in quantity; (ΔTC / ΔQ)$ $•$ $MRP of labor = Change in total revenue / Change in quantity of labor. For a firm in perfect competition, MRP of labor equals the MP of the last unit of labor times the price of the output unit. MRP = Marginal product * Product price A profit-maximizing firm will hire more labor until:$\text"MRP"_\text"Labor" = \text"Price"_\text"Labor"$Profits are maximized when:${\text"MRP"_1 / \text"Price of input 1"} = ... = {\text"MRP"_n / \text"Price of input n"} $•$ $The relationship between MR and price elasticity can be expressed as: MR =$P[1 – (1/E_P)]$In a monopoly, MC = MR so:$P[1 – (1\/E_P)]$= MC$

• Adds up the squares of the market shares of each of the largest N companies in the market. The HHI equals 1 for a monopoly. If there are M firms in the industry with equal market shares, the HHI will equal 1/M.

• Nominal GDP refers to the value of goods and services included in GDPmeasured at current prices. Nominal GDP = Quantity produced in Year t × Prices in Year t

• GDP deflator = $\text"Value of current year output at current year prices" / \text"Value of current year output at base year prices" × 100$
GDP deflator = $\text"Nominal GDP" / \text"Real GDP" × 100$

• Based on the expenditure approach, GDP may be calculated as:
GDP = C + I + G + (X × M)
C = Consumer spending on final goods and services
I = Gross private domestic investment, which includes business investment in capital goods (e.g. plant and equipment) and changes in inventory (inventory investment)
G = Government spending on final goods and services
X = Exports
M = Imports

• National income + Capital consumption allowance + Statistical discrepancy

• accounts for the wear and tear or depreciation that occurs in capital stock during the production process. It represents the amount that must be reinvested by the company in the business to maintain current productivity levels. You should think of profits + CCA as the amount earned by capital.

• $Y = AF(L,K)$ Where:

$Y$ = Aggregate output
$L$ = Quantity of labor
$K$ = Quantity of capital
$A$ = Technological knowledge or total factor productivity (TFP)

• Growth in potential GDP = Growth in technology + $W_L$(Growth in labor) + $W_K$(Growth in capital)

• Growth in technology +$W_K$(Growth in capital-labor ratio)

• Labor productivity = Real GDP/ Aggregate hours

Potential GDP = Aggregate hours × Labor productivity

This equation can be expressed in terms of growth rates as:

 Potential GDP growth rate = Long-term growth rate of labor force + Long-term labor productivity growth rate


• is calculated as:

$ULC =W\/O$

Where:

$O$ = Output per hour per worker
$W$= Total labor compensation per hour per worker



• 

Required reserve ratio = Required reserves / Total deposits

Money multiplier = 1/ (Reserve requirement)

The Fischer effect states that the nominal interest rate ($R_N$) reflects the real interest rate ($R_R$)
and the expected rate of inflation ($∏^e$).

$R_N = R_R + ∏ ^e$



• 

Ignoring taxes, the multiplier can also be calculated as:

1/(1-MPC) = 1/(1-0.9) = 10

Assuming taxes, the multiplier can also be calculated as:

$1 / [1 -\text"MPC"(1-t)]$ 

• 

A country's balance of payments is composed of three main accounts.

• The current account balance largely reflects trade in goods and services.
• The capital account balance mainly consists of capital transfers and net sales of
non-produced, non-financial assets.
• The financial account measures net capital flows based on sales and purchases of
domestic and foreign financial assets.


• 

Real exchange rate$_{DC\/FC} = S_{DC\/FC} × (P_{FC} \/ P_{DC})$

where:
$S_{DC\/FC}$ = Nominal spot exchange rate
$P_{FC}$ = Foreign price level quoted in terms of the foreign currency
$P_{DC}$ = Domestic price level quoted in terms of the domestic currency



• $F_{DC\/FC} = {1 / S_{FC\/DC}}× {(1 + r_{DC}) / (1 + r_{FC})}$ or $F_{DC\/FC} = S_{DC\/FC} ×{(1 +r_{DC}) / (1 + r_{FC})}$

Forward rates are sometimes interpreted as expected future spot rates.

$F_t = S_{t+1}$

$(S_{t+1}) / S - 1 = {Δ%S(DC\/FC)}_{t+1} = {(r_{DC} + r_{FC}) / (1 + r_{FC})}$ $•$ $ϖX εX + ϖM (εM - 1) > 0 Where: ϖX = Share of exports in total trade ϖM = Share of imports in total trade εX = Price elasticity of demand for exports εM = Price elasticity of demand for imports$ $•$ $Basic EPS =$\text"Net income – Preferred dividends" / \text"Weighted average number of shares outstanding" \$