Juan Andrés Cabral

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Repository of solved exercises and lecture notes

This space serves as a compilation of completed exercises and lecture notes that I've write over the years from teaching various courses.

Solved exercises

Two differential equations
Maximize income and minimize inputs
Double limit
Double limit 2
Characteristic polynomial, eigenvalues, and eigenvectors
Characteristic polynomial, eigenvalues, and eigenvectors 2
Characteristic polynomial, eigenvalues, and eigenvectors 3
Characteristic polynomial, eigenvalues, and eigenvectors 4
Quadratic forms and eigenvalues 1
Quadratic forms and eigenvalues 2
Characteristic Polynomial Coefficients and Their Relationship with Eigenvalues, Trace, and Determinants
Implicit derivative
Implicit derivative
Limit analysis
System of implicit equations, IS-LM Model
Derivative of a composite function
Implicit derivatives
Technical rate of substitution of an implicit function
Local optima and classification
Determining the domain in R2
Continuity at the origin
Local and global extrema
Local and global extrema 2
Differentiability at the origin
Differentiability and differentiability in a piecewise function
Double integral and reversing the order of integration
Maximum directional derivative
Economic application, first order differential equation
Elasticity and optimization
Elasticity and double integral
Elasticity and interpretation
Elasticity of implicit function
Differentiability by definition
Calculation of double, successive, and radial limits
Kuhn-tucker with two restrictions
Second-order differential equation with linear dependence in the solutions
Second-order differential equation with linear dependence in the solutions 2
Second-order differential equation with linear dependence in the solutions 3
Differential equation with separable variables
Optimization and strictly increasing transformation
Economic application of double integrals
Differential equation
Relative extrema and second order conditions
Relative extrema and second order conditions 2
Unconditioned extrema
Profit maximization with two goods and second-Order conditions
Optimization, integrals and elasticities
Clairaut-schwarz theorem
Calculate approximate value of a Function using differential
Double integrals and changing the order of integration 5
Double integrals and changing the order of integration 4
Double integrals and changing the Order of integration 3
Double integrals and changing the Order of integration 2
Double integrals and changing the Order of integration
Maximization and Minimization with Inequalities Without Using Kuhn-Tucker
Unconstrained Extrema and Second Order Condition
Homogeneous Differential Equation
Differential equation exercise
Bernoulli differential equation
Bernoulli differential equation 2
Bernoulli differential equation 3
Second order Taylor polynomial
Second order Taylor polynomial 2
Second-order Taylor polynomial for a production function
Differential equation with economic interpretation
Maximization and logarithmic transformation
Differential Equations (Separable Variables and Homogeneous)
Unclassified Ordinary Differential Equations
Maximization and Strictly Increasing Transformation
Constrained optimization with second order conditions
Constrained optimization with second order conditions 2
Conditional extremes
Sum of partial elasticities and degree of homogeneity
Double integral
Linear differential equation
Differential equation using integrating factor
Differential equation using integrating factor 2
Supply and demand model with differential equation
Price expectations model with second-order differential equations
Revenue maximization with second-order conditions
Cost minimization and interpretation of the lagrange multiplier
Optimization with constraints (multiple optimal points)
Continuity
Continuity 2
Second-Order differential equations and price expectation model
Second-order differential equation
Second-order differential equation 2
Second-order differential equation 3
First-Order differential equation
First-order differential equation 2
First-order differential equation 3
First-order differential equation 4
First-Order differential equation 5
First-Order differential equation 6
First-order differential equation 7
First-order differential equations
System of differential equations and stability
System of differential equations
Difference equation
General and particular solution of a first-order differential equation
First-Order homogeneous differential equation
Homogeneous first-order differential equations
Minimization with constraint and interpretation of lambda
Constrained minimization with second order conditions
Economic application of a second-order differential equation
Tangent plane
Second-order condition for unconstrained optimization
Types, order, and degree of differential equations
Differential equation and convergence
Classification of ordinary differential equation
Ordinary differential equation 2
Critical points and classification 2
Critical points and classification
Continuity and differentiability
Domain of a function of two variables
Derivative of composite and implicit functions
Marginal demand and elasticity with implicit function
Double limits and differentiability
Model with differential equations and convergence
Constrained optimization of a production function
Derivative of a system of implicit equations

Derivation of cost functions for Leontief technology
Substitution and income effect for cobb-douglas
Optimal production zone
Easy multiple choice
Easy multiple choice 2
Easy multiple choice 3
Easy multiple choice 4
Hicksian, expenditure function, indirect utility and Roy's lemma for cobb-douglas
Stackelberg with multiple followers
Cost function of leontief production function
Monopoly and elasticity
Monotonic transformations and preferences
Homogeneity and homotheticity of preferences
Homogeneity and homotheticity of preferences 2
Leisure-consumption preferences
Risk and expected utility
Relationship between Giffen goods and complementary goods
Aggregate supply and partial equilibrium
Cobb-douglas concavity
Elasticity and market equilibrium
Monopoly
Long run equilibrium with different technologies
Compensatory and equivalent variation of quasilinear utility
Short-run and long-run equilibrium
Producer and consumer surplus after subsidy
Duality
Price ceiling
Elasticities
"Max" utility function
Production function and perfect competition
Production function and monopoly
Tax per unit sold
Marshallian demand and hicksian demand
Cost minimization properties exercise
Marshallian demands exercise
Interpretation of a firm's graph
Income, Costs, and Profits
Slutsky and perfect substitutes
Perfect substitutes and income compensation
Profit maximization and cost minimization
Profit maximization in the short run with Cobb-Douglas
Profit maximization
Profit maximization 2
Profit maximization 3
Perfect complements combined with perfect substitutes
Technology of perfect substitutes
Hicksian demands and expenditure function for perfect complements and perfect substitutes
Exercise on duality and slutsky
Hicksian demands and expenditure function for quasilinear preferences
Marshallian, hicksian, expenditure and indirect utility functions for quasilinear preferences
Short-term profit maximization
Profit maximization with two inputs
Aggregate demand
Choice under risk
Graphical exercise on cost curves
Monopoly graphs
Compensating Variation, Equivalent Variation, and Consumer Surplus
Production function and short or long-run average costs
Expected utility and risk premium
Cost Minimization with a Cobb-Douglas Function and Second Order Conditions
Exchange economy social welfare exercise
Optimal bundle and minimum cost demonstration
Pareto efficiency and competitive equilibrium
General equilibrium with substitutes and complements
General equilibrium with substitutes and complements 2
Exchange economy and multiple equilibriums
Exchange economy exercises
Exchange economy with cobb-douglas utility
Exchange economy with indirect utility functions
Exchange economy with Cobb-Douglas and perfect substitutes
Average cost and marginal cost
Cobb-douglas production function
Intertemporal choice
Cost Minimization with Leontief technology
Corner solution production function
Indirect utility and expenditure function for min, max and perfect substitutes
Nested utility function exercise
Marshallian, hicksian, indirect utility and expenditure function of cobb-douglas
Maximizing production with second order conditions and interpretation of the Lagrange multiplier
Utility maximization with cobb-douglas
Economic interpretation of the Lagrange multiplier
Price Elasticities of Demand
Marginal rate of substitution
Bertrand competition
Cournot 2 firms linear demand
Monopolist maximization linear demand and linear cost
Monopolist maximization with quadratic costs
Stackelberg 2 firms linear demand
Utility maximization perfect complements
UUtility maximization perfect complements 2
Utility maximization perfect substitutes
Utility Maximization with Perfect Substitutes 2
Utility Maximization with Perfect Substitutes 3
Utility Maximization with Neutral and Bad Goods
Cournot N firms
Exchange economy with generic Cobb-Douglas
Cournot competition with 3 firms
Stackelberg duopoly with symmetric firms and linear demand
Substitution and income effect
Substitution and income effects for perfect complements
Monopoly and cournot
Stackelberg
Lotteries, certainty equivalent and risk premium
Cobb-Douglas maximization with second-order conditions
Classification of goods
Degree of homogeneity and substitution rates
Equivalent and compensating variation with a max Function

Lecture notes


Online Calculators

Cobb-Douglas Marshallian Demands Calculator
Perfect Complements Marshallian Demands Calculator

Books

This section contains drafts and preliminary versions of books currently in development. Please note that the material may contain errors or incomplete sections. For now, the available content is only in Spanish. Feedback and suggestions are very welcome.
Matemática aplicada 1