Mathematics for Economics and Finance - Practice Flashcards

Vocabulary flashcards covering microeconomic functions, theory of elasticity, multivariable optimization, and financial mathematics definitions and formulas.

Total Cost ($TC(Q)$)

The total economic cost incurred to produce a quantity $Q$.

Marginal Cost ($MC(Q)$)

The first-order derivative of the Total Cost function, estimating the additional cost incurred when production is increased by exactly one unit: $MC(Q) = \frac{d(T C)}{dQ} \approx T C(Q + 1) - T C(Q)$.

Total Revenue ($TR(Q)$)

The overall receipt from sales, mathematically defined as Price multiplied by Quantity: $T R(Q) = P(Q) \cdot Q$.

Marginal Revenue ($MR(Q)$)

The first-order derivative of the Total Revenue function: $MR(Q) = \frac{d(T R)}{dQ}$.

Average Cost ($AC(Q)$)

Defined as the total cost divided by the quantity produced: $AC(Q) = \frac{T C(Q)}{Q}$.

Elasticity ($E_{y,x}$)

A dimensionless, relative measure used to quantify the sensitivity of a dependent economic variable to changes in an independent variable: $E_{y,x} = \frac{dy}{dx} \times \frac{x}{y}$.

Inelastic Function

A function where the absolute value of the elasticity coefficient is less than one ($|E_{y,x}| < 1$), meaning a $1\%$ increase in $x$ leads to a change in $y$ of less than $1\%$.

Unit Elastic Function

A function where the absolute value of the elasticity coefficient is exactly one ($|E_{y,x}| = 1$), meaning a $1\%$ increase in $x$ leads to a proportional $1\%$ change in $y$.

Cross-Price Elasticity of Demand ($E_{A,B}$)

Measures the responsiveness of the quantity demanded of Good A ($Q_A$) to changes in the price of Good B ($P_B$): $E_{A,B} = \frac{\partial Q_A}{\partial P_B} \times \frac{P_B}{Q_A}$.

Complementary Goods

Goods consumed jointly characterized by a negative cross-price elasticity ($E_{A,B} < 0$), where an increase in the price of Good B decreases demand for Good A.

Substitute Goods

Goods that compete with each other characterized by a positive cross-price elasticity ($E_{A,B} > 0$), where an increase in the price of Good B increases demand for Good A.

Engel’s First Law

States that expenditures on basic food items are inelastic ($0 < E_{income} < 1$); as income increases, the proportion of income spent on food falls.

Engel’s Second Law

States that expenditures on clothing and housing are approximately unit elastic ($E_{income} \approx 1$), meaning the budget proportion for these remains relatively constant as income shifts.

Hessian Determinant ($H$)

The determinant of the Hessian matrix used to check for local extrema: $H = f_{xx}f_{yy} - (f_{xy})^2$. If $H > 0$ and $f_{xx} > 0$, it is a local minimum; if $H > 0$ and $f_{xx} < 0$, it is a local maximum.

Saddle Point

The classification of a point in multivariable calculus when the Hessian determinant is negative ($H < 0$).

Returns to Scale

Determined by the degree of homogeneity $k$ ($\lambda$) of a production function: $k = 1$ is constant, $k > 1$ is increasing, and $k < 1$ is decreasing returns to scale.

Lagrangian Optimization

A method to optimize an objective function $f(x, y)$ subject to an equality constraint $g(x, y) = c$ by defining the function $L(x, y, \lambda) = f(x, y) + \lambda(c - g(x, y))$.

Lagrange Multiplier ($\lambda$)

Represents the shadow price or rate of change of the optimal value of the objective function with respect to the constraint constant: $\lambda = \frac{\partial f^*}{\partial c}$.

Simple Interest

Interest computed solely on the initial principal $C_0$ that is not added to the principal to earn further interest: $I = C_0 \times i \times t$.

Compound Interest

A model where accrued interest is added to the principal at the end of each period to compound the interest base: $C_t = C_0(1 + i)^t$.

Decursive Compounding

Interest calculated at the end of each period relative to the starting principal of that period.

Anticipative Compounding

Interest calculated at the beginning of each period based on the final anticipated value at the end of the period, used in banking discount procedures.

Relative Interest Rate ($i_{rel}$)

A simple linear subdivision of the nominal annual rate $r$ over $m$ periods: $i_{rel} = \frac{r}{m}$.

Conforming Interest Rate ($i_{conf}$)

The mathematically correct rate ensuring the future value under sub-period compounding matches the annual compounding rate exactly: $i_{conf} = (1 + r)^{\frac{1}{m}} - 1$.

Continuous Compounding

A model where compounding occurs as intervals approach infinity ($m \rightarrow \infty$), defined as $F V = P V \cdot e^{rt}$, where $e \approx 2.71828$.

Payment Quota ($R_t$)

The portion of an annuity that accounts for principal repayment, directly reducing the outstanding principal balance.

Prenumerando (Annuity Due)

Equal payments or installments processed at the beginning of each compounding period.

Postnumerando (Ordinary Annuity)

Equal payments or installments processed at the end of each compounding period.

Loan Conversion

The legal modification or formal amendment of an active loan's amortization schedule, such as changing interest rates or extending tenure.

Dogovoreni anuiteti (Agreed Equal Annuities)

Fixed payments at a rounded, arbitrary value established by contract, requiring the final period to have an adjusted payment to clear the residual debt.

German Method (30/360)

A day-count method where each calendar month is treated as exactly $30$ days and the year as $360$ days.

Bill of Exchange

A formal, written document used in commerce that binds one party to pay a fixed sum of money to another party at a designated date.

What is Total Cost ($TC(Q)$)?

The total economic cost incurred to produce a quantity $Q$.

What is Marginal Cost ($MC(Q)$)?

The first-order derivative of the Total Cost function, estimating the additional cost incurred when production is increased by exactly one unit: $MC(Q) = \\frac{d(T C)}{dQ} \\approx T C(Q + 1) - T C(Q).$

What is Total Revenue ($TR(Q)$)?

The overall receipt from sales, mathematically defined as Price multiplied by Quantity: $T R(Q) = P(Q) \\cdot Q.$

What is Marginal Revenue ($MR(Q)$)?

The first-order derivative of the Total Revenue function: $MR(Q) = \\frac{d(T R)}{dQ}.$

What is Average Cost ($AC(Q)$)?

Defined as the total cost divided by the quantity produced: $AC(Q) = \\frac{T C(Q)}{Q}.$

What is Elasticity ($E\\_{y,x}$)?

A dimensionless, relative measure used to quantify the sensitivity of a dependent economic variable to changes in an independent variable: $E\\_{y,x} = \\frac{dy}{dx} \\times \\frac{x}{y}.$

What is an Inelastic Function?

A function where the absolute value of the elasticity coefficient is less than one ($\\|E\\_{y,x}\\| < 1$), meaning a $1\\%$ increase in $x$ leads to a change in $y$ of less than $1\\%.$

What is a Unit Elastic Function?

A function where the absolute value of the elasticity coefficient is exactly one ($\\|E\\_{y,x}\\| = 1$), meaning a $1\\%$ increase in $x$ leads to a proportional $1\\%$ change in $y.$

What is Cross-Price Elasticity of Demand ($E\\_{A,B}$)?

Measures the responsiveness of the quantity demanded of Good A ($Q\\_A$) to changes in the price of Good B ($P\\_B$): $E\\_{A,B} = \\frac{\\partial Q\\_A}{\\partial P\\_B} \\times \\frac{P\\_B}{Q\\_A}.$

What are Complementary Goods?

Goods consumed jointly characterized by a negative cross-price elasticity ($E\\_{A,B} < 0$), where an increase in the price of Good B decreases demand for Good A.

What are Substitute Goods?

Goods that compete with each other characterized by a positive cross-price elasticity ($E\\_{A,B} > 0$), where an increase in the price of Good B increases demand for Good A.

What is Engel’s First Law?

States that expenditures on basic food items are inelastic ($0 < E\\_{income} < 1$); as income increases, the proportion of income spent on food falls.

What is Engel’s Second Law?

States that expenditures on clothing and housing are approximately unit elastic ($E\\_{income} \\approx 1$), meaning the budget proportion for these remains relatively constant as income shifts.

What is the Hessian Determinant ($H$)?

The determinant of the Hessian matrix used to check for local extrema: $H = f\\_{xx}f\\_{yy} - (f\\_{xy})^2$. If $H > 0$ and $f\\_{xx} > 0$, it is a local minimum; if $H > 0$ and $f\\_{xx} < 0$, it is a local maximum.

What is a Saddle Point?

The classification of a point in multivariable calculus when the Hessian determinant is negative ($H < 0$).

What are Returns to Scale?

Determined by the degree of homogeneity $k$ ($\\lambda$) of a production function: $k = 1$ is constant, $k > 1$ is increasing, and $k < 1$ is decreasing returns to scale.

What is Lagrangian Optimization?

A method to optimize an objective function $f(x, y)$ subject to an equality constraint $g(x, y) = c$ by defining the function $L(x, y, \\lambda) = f(x, y) + \\lambda(c - g(x, y))$.

What is the Lagrange Multiplier ($\\lambda$)?

Represents the shadow price or rate of change of the optimal value of the objective function with respect to the constraint constant: \\lambda = \\frac{\\partial f^\\*}{\\partial c}.

What is Simple Interest?

Interest computed solely on the initial principal $C\\_0$ that is not added to the principal to earn further interest: $I = C\\_0 \\times i \\times t.$

What is Compound Interest?

A model where accrued interest is added to the principal at the end of each period to compound the interest base: $C\\_t = C\\_0(1 + i)^t.$

What is Decursive Compounding?

Interest calculated at the end of each period relative to the starting principal of that period.

What is Anticipative Compounding?

Interest calculated at the beginning of each period based on the final anticipated value at the end of the period, used in banking discount procedures.

What is Relative Interest Rate ($i\\_{rel}$)?

A simple linear subdivision of the nominal annual rate $r$ over $m$ periods: $i\\_{rel} = \\frac{r}{m}.$

What is Conforming Interest Rate ($i\\_{conf}$)?

The mathematically correct rate ensuring the future value under sub-period compounding matches the annual compounding rate exactly: $i\\_{conf} = (1 + r)^{\\frac{1}{m}} - 1.$

What is Continuous Compounding?

A model where compounding occurs as intervals approach infinity ($m \\rightarrow \\infty$), defined as $F V = P V \\cdot e^{rt}$, where $e \\approx 2.71828.$

What is Payment Quota ($R\\_t$)?

The portion of an annuity that accounts for principal repayment, directly reducing the outstanding principal balance.

What is Prenumerando (Annuity Due)?

Equal payments or installments processed at the beginning of each compounding period.

What is Postnumerando (Ordinary Annuity)?

Equal payments or installments processed at the end of each compounding period.

What is Loan Conversion?

The legal modification or formal amendment of an active loan's amortization schedule, such as changing interest rates or extending tenure.

What are Dogovoreni anuiteti (Agreed Equal Annuities)?

Fixed payments at a rounded, arbitrary value established by contract, requiring the final period to have an adjusted payment to clear the residual debt.

What is the German Method (30/360)?

A day-count method where each calendar month is treated as exactly $30$ days and the year as $360$ days.

What is a Bill of Exchange?

A formal, written document used in commerce that binds one party to pay a fixed sum of money to another party at a designated date.