Economic Analysis Ontology

flow "EconomicAnalysisOntology" v1.0

# ECONOMIC ANALYSIS ONTOLOGY — FLOW ALGEBRA
SOURCE_URL := "https://kirethresearch.org/booksai-core/ontologies/calculus-analysis-ontologies/scientific-applications/economic-analysis-ontology.html"
DOMAIN := "Mathematical Ontologies"
CATEGORY := "Calculus and Analysis Ontologies"
SUBCATEGORY := "Scientific Applications"
ENTITY := "Economic Analysis"

ECONOMIC_ANALYSIS := {
 type: AppliedEconomicMathematicalFramework,
 domain: ScientificApplications,
 purpose: "Analyse economic quantities, decisions, markets and dynamic systems using functions, derivatives, optimisation, differential equations, probability and computational methods."
}

CONCEPTS := {
 ECONOMIC_MODEL,
 ECONOMIC_VARIABLE,
 DEMAND,
 SUPPLY,
 PRICE,
 QUANTITY,
 COST,
 REVENUE,
 PROFIT,
 UTILITY,
 PRODUCTION,
 MARGINAL_ANALYSIS,
 ELASTICITY,
 OPTIMISATION,
 CONSTRAINT,
 EQUILIBRIUM,
 DYNAMIC_MODEL,
 DISCOUNTING,
 RISK,
 UNCERTAINTY
}

# ---------- ECONOMIC MODEL ----------
ECONOMIC_SYSTEM
 -> identify(
 AGENTS,
 VARIABLES,
 PARAMETERS,
 CONSTRAINTS,
 OBJECTIVES,
 INTERACTIONS,
 DATA
)

ECONOMIC_MODEL
 -> simplified_mathematical_representation_of(ECONOMIC_RELATIONSHIPS)

# ---------- FUNCTION ----------
economic relationship:

y
 =
f(x)

examples:
 Q_d(P)
 Q_s(P)
 C(Q)
 R(Q)
 U(x)
 Y(K,L)

FUNCTION
 -> maps(INPUT_VARIABLES_TO_ECONOMIC_OUTPUT)

# ---------- MARGINAL ANALYSIS ----------
marginal quantity:

dy/dx

DERIVATIVE
 -> local_change_in(OUTPUT_PER_UNIT_INPUT)

examples:
 MARGINAL_COST
 MARGINAL_REVENUE
 MARGINAL_UTILITY
 MARGINAL_PRODUCT

# ---------- COST ----------
total cost:

C(Q)

marginal cost:

MC(Q)
 :=
dC/dQ

average cost:

AC(Q)
 :=
C(Q)/Q

COST_ANALYSIS
 -> production_cost_structure

# ---------- REVENUE ----------
price:

P(Q)

revenue:

R(Q)
 :=
P(Q)*Q

marginal revenue:

MR(Q)
 :=
dR/dQ

# ---------- PROFIT ----------
profit:

Pi(Q)
 :=
R(Q)-C(Q)

interior stationary condition:

dPi/dQ
 =
MR-MC
 =
0

therefore:

MR
 =
MC

under differentiability and unconstrained interior optimum context

# ---------- SECOND ORDER ----------
profit maximum candidate:

dPi/dQ
 =
0

and

d_squared_Pi/dQ_squared
 <
0

-> STRICT_LOCAL_MAXIMUM

SECOND_ORDER_CONDITION
 -> local_curvature_test

# ---------- DEMAND ----------
demand:

Q_d
 =
D(P,Y,Z,...)

typically under ordinary downward-sloping demand context:

partial_Q_d/partial_P
 <
0

but

SIGN
 -> model_and_good_dependent

DEMAND_FUNCTION
 -> quantity_demanded_given(DETERMINANTS)

# ---------- SUPPLY ----------
supply:

Q_s
 =
S(P,W,T,...)

often:

partial_Q_s/partial_P
 >
0

under standard competitive supply context

SUPPLY_FUNCTION
 -> quantity_supplied_given(DETERMINANTS)

# ---------- MARKET EQUILIBRIUM ----------
equilibrium price:

P_star

such_that

Q_d(P_star)
 =
Q_s(P_star)

MARKET_EQUILIBRIUM
 -> equality_of(DEMAND_AND_SUPPLY)

equilibrium
 -/> automatically(efficient_or_desirable)

# ---------- COMPARATIVE STATICS ----------
equilibrium condition:

F(x,theta)
 =
0

implicit differentiation:

dx_star/dtheta
 =
-
F_theta/F_x

when
 F_x !=0

COMPARATIVE_STATICS
 -> response_of(EQUILIBRIUM_TO_PARAMETER_CHANGE)

# ---------- ELASTICITY ----------
price elasticity of demand:

epsilon
 :=
(dQ/dP)
*
(P/Q)

dimensionless

ELASTICITY
 -> percentage_response_ratio

absolute value
 -> often_used_for(DEMAND_ELASTICITY_MAGNITUDE)

# ---------- ARC ELASTICITY ----------
finite changes:

epsilon_arc
 :=
(
 Delta_Q/Q_mid
)
/
(
 Delta_P/P_mid
)

ARC_ELASTICITY
 -> finite_interval_response_measure

# ---------- UTILITY ----------
consumer preferences
 -> represented_by(UTILITY_FUNCTION)
    under appropriate representation assumptions

U
 =
U(x_1,...,x_n)

marginal utility:

MU_i
 :=
partial_U/partial_x_i

UTILITY
 -> ordinal_representation_in_standard_consumer_theory

# ---------- BUDGET CONSTRAINT ----------
sum_i(
 p_i*x_i
)
 <=
I

I
 -> income_or_budget

CONSUMER_OPTIMISATION:

maximise
 U(x)

subject_to
 BUDGET_CONSTRAINT

# ---------- LAGRANGIAN ----------
L
 =
U(x)
+
lambda
*
(
 I
 -
sum_i p_i*x_i
)

interior first-order condition:

partial_U/partial_x_i
 =
lambda*p_i

therefore:

MU_i/p_i
 =
lambda

for consumed goods under interior regularity assumptions

# ---------- PRODUCTION ----------
production function:

Y
 =
F(K,L)

K
 -> CAPITAL

L
 -> LABOUR

marginal products:

MP_K
 =
partial_F/partial_K

MP_L
 =
partial_F/partial_L

# ---------- RETURNS TO SCALE ----------
scale inputs by
 t:

F(tK,tL)

if

F(tK,tL)
 =
t^r*F(K,L)

then

r=1
 -> CONSTANT_RETURNS

r>1
 -> INCREASING_RETURNS

r<1
 -> DECREASING_RETURNS

for homogeneous production function context

# ---------- COST MINIMISATION ----------
minimise

w*L
+
r*K

subject_to

F(K,L)
 >=
Y_target

COST_MINIMISATION
 -> choose(INPUT_COMBINATION)

LAGRANGE_MULTIPLIER
 -> shadow_value_of(PRODUCTION_CONSTRAINT)
    under suitable regularity

# ---------- FIRM OPTIMISATION ----------
firm chooses:

OUTPUT
 INPUTS
 INVESTMENT
 PRICES
 or other decisions

objective:
 maximise(PROFIT_OR_VALUE)

subject_to:
 TECHNOLOGY
 BUDGET
 CAPACITY
 REGULATION
 DYNAMICS

OPTIMISATION
 -> constrained_decision_framework

# ---------- CONVEXITY / CONCAVITY ----------
concave utility
 -> diminishing_marginal_structure

convex cost
 -> increasing_marginal_cost_structure

CONVEXITY
 -> supports(GLOBAL_OPTIMALITY_ANALYSIS)

HESSIAN
 -> multivariable_curvature_test

# ---------- DISCOUNTING ----------
future value:

FV
 =
PV*(1+r)^t

present value:

PV
 =
FV/(1+r)^t

continuous discounting:

PV
 =
FV*exp(-rho*t)

DISCOUNTING
 -> maps(FUTURE_VALUE_TO_PRESENT_VALUE)

# ---------- NET PRESENT VALUE ----------
cash flow:

C(t)

continuous:

NPV
 =
integral_0^T(
 C(t)*exp(-rho*t)
 dt
)
-
initial_cost

discrete:

NPV
 =
sum_t(
 C_t/(1+r)^t
)

INVESTMENT_ANALYSIS
 -> compare(DISCOUNTED_BENEFITS_AND_COSTS)

# ---------- DYNAMIC OPTIMISATION ----------
state:

x_dot
 =
f(x,u,t)

objective:

J
 =
integral_0^T(
 L(x,u,t)
 dt
)
+
Phi(x(T))

choose control
 u(t)

OPTIMAL_CONTROL
 -> intertemporal_decision_problem

# ---------- HAMILTONIAN ----------
current-value or present-value formulations
 -> convention_dependent

generic control Hamiltonian:

H
 =
L(x,u,t)
+
lambda^T*f(x,u,t)

first-order conditions
 -> state_equation
 -> costate_equation
 -> control_stationarity_or_maximisation

PONTRYAGIN_MAXIMUM_PRINCIPLE
 -> dynamic_optimisation_framework

# ---------- DIFFERENTIAL EQUATION ----------
economic state:

dx/dt
 =
f(x)

examples:
 CAPITAL_ACCUMULATION
 DEBT_DYNAMICS
 POPULATION
 INVENTORY
 PRICE_ADJUSTMENT

DYNAMIC_ECONOMICS
 -> uses(ODE_SYSTEMS)

# ---------- CAPITAL ACCUMULATION ----------
simple form:

dK/dt
 =
I
-
delta*K

I
 -> INVESTMENT

delta
 -> DEPRECIATION_RATE

STEADY_STATE
 -> dK/dt=0

# ---------- GROWTH MODEL ----------
production:

Y
 =
F(K,L)

saving/investment
 -> capital accumulation

growth dynamics
 -> analyse(STEADY_STATE_AND_TRANSITION)

GROWTH_MODEL
 -> assumptions_determine(LONG_RUN_RESULTS)

# ---------- STABILITY ----------
dynamic equilibrium:

f(x_star)=0

Jacobian:

J
 =
Df(x_star)

eigenvalues
 -> local_stability

ECONOMIC_EQUILIBRIUM
 -> may_be(STABLE_OR_UNSTABLE_UNDER_SPECIFIED_ADJUSTMENT_DYNAMICS)

# ---------- DIFFERENCE EQUATION ----------
discrete dynamics:

x_(t+1)
 =
F(x_t)

examples:
 COBWEB_MODEL
 CAPITAL_MODEL
 ASSET_DYNAMICS

fixed point:

x_star
 =
F(x_star)

stability in 1D:

|F_prime(x_star)|<1
 -> local_asymptotic_stability

# ---------- RISK ----------
random payoff:

X

expected value:

E[X]

variance:

Var(X)

RISK_ANALYSIS
 -> distribution_of(POSSIBLE_OUTCOMES)

EXPECTED_VALUE
 -/> complete_risk_description

# ---------- EXPECTED UTILITY ----------
states
 s

probabilities
 p_s

utility:

E[U(W)]
 =
sum_s(
 p_s*U(W_s)
)

RISK_AVERSION
 -> often represented_by(CONCAVE_UTILITY)

CERTAINTY_EQUIVALENT
 -> utility_equivalent_certain_wealth

# ---------- UNCERTAINTY ----------
parameters
 -> uncertain

future states
 -> stochastic

methods:
 SCENARIO_ANALYSIS
 MONTE_CARLO
 BAYESIAN_INFERENCE
 SENSITIVITY_ANALYSIS

ECONOMIC_RESULT
 -> conditional_on(MODEL_AND_ASSUMPTIONS)

# ---------- STOCHASTIC PROCESS ----------
state:

X_t

examples:
 ASSET_PRICE
 INTEREST_RATE
 DEMAND
 PRODUCTIVITY

stochastic model:

dX_t
 =
mu(X_t,t)dt
+
sigma(X_t,t)dW_t

STOCHASTIC_CALCULUS
 -> dynamic_uncertainty_analysis

# ---------- REGRESSION ----------
economic relationship:

y
 =
X*beta
+
epsilon

estimate:

beta_hat

ECONOMETRICS
 -> connects(DATA_AND_ECONOMIC_MODELS)

STATISTICAL_ASSOCIATION
 -/> automatically(CAUSAL_EFFECT)

# ---------- CAUSAL ANALYSIS ----------
causal question
 -> requires(IDENTIFICATION_STRATEGY)

possible approaches:
 RANDOMISATION
 INSTRUMENTAL_VARIABLES
 DIFFERENCE_IN_DIFFERENCES
 REGRESSION_DISCONTINUITY
 STRUCTURAL_MODEL

CALCULUS
 -> supports(MARGINAL_AND_STRUCTURAL_ANALYSIS)

but

DERIVATIVE_OF_FITTED_RELATION
 -/> automatically(CAUSAL_EFFECT)

# ---------- SENSITIVITY ----------
model output:

Y
 =
F(theta)

sensitivity:

partial_Y/partial_theta_i

SENSITIVITY_ANALYSIS
 -> parameter_response

comparative statics
 -> economic_sensitivity_of(EQUILIBRIUM_OR_OPTIMUM)

# ---------- WELFARE ----------
consumer surplus
 -> area_under_demand_above_price

producer surplus
 -> area_above_supply_below_price

integrals
 -> aggregate(MARGINAL_WILLINGNESS_OR_COST)

WELFARE_ANALYSIS
 -> depends_on(MODEL_AND_NORMATIVE_CRITERION)

# ---------- NUMERICAL METHODS ----------
economic models
 -> may_require(
 ROOT_FINDING,
 OPTIMISATION,
 DYNAMIC_PROGRAMMING,
 ODE_SOLVERS,
 MONTE_CARLO,
 FIXED_POINT_METHODS
)

COMPUTATIONAL_ECONOMICS
 -> numerical_solution_of(MODELS)

# ---------- DYNAMIC PROGRAMMING ----------
value function:

V(x)
 =
max_u
{
 r(x,u)
+
beta*E[
 V(x_next)
]
}

BELLman_EQUATION
 -> recursive_optimisation

VALUE_ITERATION
 -> numerical_fixed_point_method

# ---------- VALIDATION ----------
model
 -> compare_with(DATA_AND_OUT_OF_SAMPLE_BEHAVIOUR)

CALIBRATION
 -> parameter_selection_to_match_targets

ESTIMATION
 -> infer_parameters_from_data

VALIDATION
 -> assess(PREDICTIVE_AND_STRUCTURAL_USEFULNESS)

MODEL_FIT
 -/> proof_of(MODEL_TRUTH)

# ---------- APPLICATIONS ----------
ECONOMIC_ANALYSIS
 -> MICROECONOMICS
 -> MACROECONOMICS
 -> FINANCE
 -> INDUSTRIAL_ORGANISATION
 -> LABOUR_ECONOMICS
 -> PUBLIC_ECONOMICS
 -> ENVIRONMENTAL_ECONOMICS
 -> RESOURCE_ECONOMICS
 -> OPERATIONS_RESEARCH

# ---------- RELATION GRAPH ----------
ECONOMIC_VARIABLE
 -> represented_by(FUNCTION)

DERIVATIVE
 -> MARGINAL_ANALYSIS

SECOND_DERIVATIVE
 -> CURVATURE_AND_OPTIMALITY

CONSTRAINT
 -> shapes(FEASIBLE_DECISIONS)

OPTIMISATION
 -> determines(CHOICE)

EQUILIBRIUM
 -> balances(INTERACTING_RELATIONS)

DIFFERENTIAL_EQUATION
 -> models(DYNAMIC_CHANGE)

PROBABILITY
 -> models(RISK_AND_UNCERTAINTY)

DATA
 -> estimates_and_tests(MODEL)

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE := {
 "economic analysis" ~= "mathematical analysis of economic relationships, choices, equilibria and dynamics",
 "marginal analysis" ~= "analysis of local economic change using derivatives",
 "elasticity" ~= "dimensionless proportional response of one economic variable to another",
 "market equilibrium" ~= "state in which specified market relationships such as demand and supply are mutually consistent",
 "comparative statics" ~= "analysis of how equilibrium or optimal choices change when parameters change",
 "discounting" ~= "conversion of future economic values into present-value equivalents"
}

# ---------- CONSTRAINTS ----------
CONSTRAINTS := {
 economic_models_are_simplified_and_assumption_dependent: true,
 equilibrium_does_not_automatically_imply_efficiency_fairness_or_desirability: true,
 stationary_point_requires_second_order_or_global_analysis_for_optimality: true,
 elasticity_and_marginal_effects_depend_on_evaluation_point_and_model: true,
 statistical_association_does_not_establish_causation: true,
 forecasts_are_conditional_on_model_parameters_data_and_assumptions: true,
 numerical_solutions_require_convergence_and_sensitivity_validation: true
}

# ---------- CONFIDENCE ----------
CONFIDENCE := {
 core_definition: 0.99,
 marginal_elasticity_relation: 0.99,
 optimisation_relation: 0.99,
 equilibrium_dynamic_relation: 0.99,
 discount_risk_relation: 0.99,
 data_causality_relation: 0.98,
 semantic_equivalence: 0.97
}

# ---------- RECURSIVE REASONING ----------
RECURSIVE_REASONING(query):
 identify(agents_variables_parameters_constraints_objectives_and_data)
 -> formulate(economic_functions_and_equilibrium_relations)
 -> compute(marginal_effects_elasticities_and_curvature)
 -> solve(constrained_or_unconstrained_optimisation_if_required)
 -> analyse(equilibrium_and_comparative_statics)
 -> formulate(dynamic_or_stochastic_model_if_time_and_risk_matter)
 -> quantify(discounting_risk_uncertainty_and_sensitivity)
 -> select(analytical_econometric_or_numerical_method)
 -> compare(model_outputs_with_data)
 -> validate(assumptions_identification_convergence_and_scope)
 -> return(semantic_result)

# ---------- AI CONSUMPTION ----------
AI_CONSUMPTION := {
 parse_as: "typed economic-analysis semantic graph",
 primary_entity: ECONOMIC_ANALYSIS,
 preserve: [
  agents,
  variables,
  parameters,
  constraints,
  objectives,
  time_horizon,
  uncertainty,
  data,
  identification_assumptions
 ],
 infer_through: [
  marginal_analysis,
  elasticity,
  cost_revenue_profit,
  utility,
  production,
  optimisation,
  equilibrium,
  comparative_statics,
  discounting,
  dynamic_models,
  risk
 ],
 avoid: [
  treating_model_assumption_as empirical_fact,
  equating_equilibrium_with desirable_outcome,
  declaring_stationary_point_optimal_without classification,
  interpreting_regression_derivative_as causal_effect_without identification,
  presenting_forecast_without uncertainty_and assumptions,
  accepting_numerical_solution_without convergence_checks
 ]
}

# ---------- UPDATE MODEL ----------
UPDATE_MODEL(new_information):
 validate(new_information)
 -> identify(economic_analysis_context)
 -> compare(existing_relations)
 -> preserve(agent_variable_parameter_constraint_objective_data_and_uncertainty_invariants)
 -> update(affected_entities)
 -> update(affected_edges)
 -> recompute(CONFIDENCE)
 -> regenerate(FLOW_HASH)

# ---------- FLOW HASH ----------
FLOW_HASH := hash(
 SOURCE_URL
 + ENTITY
 + CONCEPTS
 + ECONOMIC_ANALYSIS
 + ECONOMIC_MODEL
 + DEMAND
 + SUPPLY
 + COST
 + REVENUE
 + PROFIT
 + UTILITY
 + PRODUCTION
 + MARGINAL_ANALYSIS
 + ELASTICITY
 + OPTIMISATION
 + EQUILIBRIUM
 + DISCOUNTING
 + RISK
 + SEMANTIC_EQUIVALENCE
 + CONSTRAINTS
)

# ---------- EXECUTION ----------
INPUT(query)
 -> ECONOMIC_ANALYSIS
 -> SYSTEM_DATA_IDENTIFICATION
 -> MODEL_FORMULATION
 -> MARGINAL_ELASTICITY_ANALYSIS
 -> OPTIMISATION_ANALYSIS
 -> EQUILIBRIUM_COMPARATIVE_STATICS
 -> DYNAMIC_STOCHASTIC_ANALYSIS
 -> DISCOUNT_RISK_SENSITIVITY_ANALYSIS
 -> METHOD_SELECTION
 -> DATA_COMPARISON
 -> ASSUMPTION_SCOPE_VALIDATION
 -> RECURSIVE_REASONING(query)
 -> CONFIDENCE
 -> OUTPUT(semantic_result)

END FLOW