Computational economics uses algorithms to solve, simulate and investigate economic models. It is useful when interacting choices, uncertainty, constraints or time make an exact hand calculation impractical. Its gold standard is a result that another person can reproduce, check against the model's equations and interpret within the model's limits.
A computer can calculate an equilibrium without proving that a real market will reach it. It can find an optimal choice under stated preferences without establishing what society ought to value. This guide makes those distinctions concrete through original fictional examples. All numerical quantities below are teaching assumptions, not measurements of an actual economy or recommendations about investments.
Begin with the Gold Standard master, connect the exercises to Education: learning that transfers into life, or explore the How X Works hub. The Economics root explains choices and institutions. Here the question is more specific: how do we obtain a numerical answer to an economic model, and what evidence tells us that answer is dependable?
Choose your computational economics route
Follow a model from its equations to a checked numerical answer and an economic interpretation.
Route 1 · Chapters 1–4: Specify and solve a market
Route 2 · Chapters 5–7: Follow adjustment and decisions
Route 3 · Chapters 8–10: Compute distributions and approximations
Route 4 · Chapters 11–12: Compare policies and diagnose errors
Route 5 · Chapters 13–14: Transfer and continue learning
Chapter index
Specify and solve a market · Chapters 1–4
1. Separate the economic question from the computation
2. Build a model whose quantities can be checked
Follow adjustment and decisions · Chapters 5–7
5. Distinguish equilibrium from the path towards it
Compute distributions and approximations · Chapters 8–10
8. Compute distributions rather than only averages
Compare policies and diagnose errors · Chapters 11–12
Transfer and continue learning · Chapters 13–14
CHAPTER 1 OF 14 · Specify and solve a market
1. Separate the economic question from the computation
Suppose a town wants to understand how a delivery charge might change the quantity traded in a local market. There are several different tasks hiding inside that sentence. Someone must define the market and its participants. Someone must decide which behavioural relationships are defensible. Someone must estimate or otherwise justify their parameters. Only then can a numerical procedure solve the chosen equations.
Computational economics works at the intersection of these tasks, but completing one does not complete the others. A solver might accurately calculate the implications of an implausible demand curve. An excellent empirical estimate may still be combined with the wrong accounting identity. A simulation might faithfully implement a model whose rules omit the institution that matters most.
Four questions to write before coding
What is being calculated: a price, an allocation, a decision rule, a distribution or a path through time? What conditions define a valid answer? Which inputs are observed, estimated or assumed? What comparison would make the result useful? These questions determine whether the task is root finding, optimisation, dynamic programming, simulation or some combination.
For the delivery-charge question, one model might calculate the price at which planned supply equals planned demand. Another might model sellers adjusting prices over many days. These models can share an equilibrium yet disagree about the adjustment path. The first answers a consistency question; the second adds behavioural assumptions about change.
The Econometrics guide is the route into estimation, measurement and causal evidence. The Scientific Computing guide explains numerical reliability across disciplines. Computational economics adds the particular economic restrictions: budgets must balance, choices must be feasible, incentives must be represented and aggregate quantities must agree with individual decisions.
A useful first deliverable is therefore a one-page model description rather than a large program. Write the units, timing and equation meanings in ordinary language. If two colleagues disagree about whether a price is paid by buyers or received by sellers, no increase in computing power will resolve that ambiguity.
CHAPTER 2 OF 14 · Specify and solve a market
2. Build a model whose quantities can be checked
Consider an invented market for a divisible good. Let p be its price in currency units per unit of the good. Daily demand is D(p) = 120 − 4p and daily supply is S(p) = 20 + 6p. Restrict attention to prices between 0 and 30 so the demand expression is nonnegative. The numbers are deliberately simple enough to provide an exact benchmark.
Market clearing requires D(p) = S(p). Subtracting supply from demand gives the excess-demand function z(p) = 100 − 10p. Its zero is p = 10. Substituting into both original equations gives demand 80 and supply 80 units per day. Those substitutions matter: reporting only the price conceals whether the underlying quantities agree.
Check dimensions before checking precision
The intercepts 120 and 20 have units of goods per day. The slope coefficients have units that convert a price change into a daily quantity change. The residual z(p) also has quantity-per-day units. A tolerance of 0.001 applied to the price and a tolerance of 0.001 applied to excess demand are therefore different requirements.
A spreadsheet can place the price in one cell, demand and supply in two more, and their difference in a fourth. Before introducing an automatic solver, test prices 0, 10 and 20. The residuals should be 100, 0 and −100. These checks reveal a reversed sign, a missing coefficient or a mistaken cell reference immediately.
The model has important exclusions. It assumes a homogeneous divisible good, a single price and no shortage allocation rule, capacity discontinuity or transaction timing problem. It says nothing about whether the equilibrium is fair. It also does not say how the demand and supply curves were measured.
This is a small model, not a small standard of evidence. A more complicated implementation should retain similarly clear checks. For another example of why definitions matter, the specialist guide to real exchange rates and inflation differences distinguishes nominal movements from a price-adjusted comparison. The same discipline applies when choosing model units. Record what each array represents, which index denotes an individual or period, and how totals are constructed. Numerical work becomes difficult to audit when those meanings exist only in the programmer's memory.
CHAPTER 3 OF 14 · Specify and solve a market
3. Find a market-clearing price without guessing blindly
For the linear market above, algebra is the best first solution. Numerical methods become useful when z(p) contains nonlinear expressions, numerical expectations or many interacting markets. The simple example remains valuable because it lets us test a numerical routine against a known answer.
A bracket is an interval whose endpoints give residuals of opposite signs. In our market, z(0) = 100 and z(15) = −50. Because the function is continuous, there is at least one zero between those endpoints. Bisection evaluates the midpoint and retains a half-interval containing a sign change. It is systematic rather than a search for a visually pleasing graph.
A hand-checkable sequence
The first midpoint is 7.5, giving z = 25, so retain [7.5, 15]. The next midpoint is 11.25, giving −12.5, so retain [7.5, 11.25]. The third is 9.375, giving 6.25. The interval narrows around 10. After n halvings, its width is 15 divided by 2 to the power n; the midpoint is at most half that width from a root retained in the bracket.
After ten halvings the width is approximately 0.01465 price units. That is a numerical enclosure, not an economic confidence interval. It says nothing about uncertainty in the coefficients 120, 4, 20 and 6. Confusing those two kinds of uncertainty creates a false appearance of empirical precision.
SciPy's official Brent-method documentation specifies continuity and opposite endpoint signs for its bracketed root finder. It also distinguishes absolute and relative tolerances and exposes convergence information. These are conditions to inspect, not settings to copy without considering units.
A sign change alone is insufficient when the function is discontinuous. A jump from positive to negative can skip zero entirely. Conversely, a function can touch zero without changing sign. Before choosing a method, inspect the mathematical structure. If a model contains discrete choices, a capacity cap or a tax threshold, explain how those features affect the solver's assumptions.
CHAPTER 4 OF 14 · Specify and solve a market
4. Understand Newton steps and their failure modes
Newton's method uses a local slope to predict where a function will cross zero. For a differentiable excess-demand function, the update is p_new = p_old − z(p_old)/z′(p_old), provided the derivative is usable. It can be fast near a suitable solution, but it is not a universal guarantee of convergence.
In the linear example, start at p = 3. The residual is 70 and the slope is −10. The update gives 3 − 70/(−10) = 10. One step reaches the exact root because the linear approximation is the function itself. That success should not be extrapolated to every economic model.
A nonlinear exercise
Suppose an alternative teaching residual is z(p) = 100 − p², with admissible prices p greater than zero. Starting at p = 6 gives z = 64 and z′ = −12, so the next estimate is approximately 11.3333. The following step is approximately 10.0784, and another is approximately 10.0003. Direct substitution checks how rapidly the residual shrinks.
Starting at zero makes the derivative zero, so the formula cannot be used. An unrestricted numerical procedure could also find the mathematical root −10, which is outside the stated admissible price domain. Finding a root and finding an economically admissible root are separate checks.
QuantEcon's Newton-method lecture connects zero finding and fixed-point calculations to economic models. Use it for the method and its implementation. In practical work, record initial guesses and test more than one plausible starting point when multiple solutions or difficult nonlinearities may matter.
Repair begins with diagnosis. A very large step may indicate a nearly flat derivative, unsuitable scaling or a poor starting point. Reducing the step, using a bracketed method where its conditions hold, or reformulating variables can help. None of those repairs justifies silently replacing an economic constraint. If the model only permits nonnegative quantities, a negative result must be rejected or the model must be explicitly changed.
CHAPTER 5 OF 14 · Follow adjustment and decisions
5. Distinguish equilibrium from the path towards it
An equilibrium equation describes mutual consistency. An adjustment rule describes movement. The two should not be conflated. Suppose prices follow the invented rule p_next = p + λz(p), where λ is a positive adjustment coefficient. Sellers raise prices when planned demand exceeds planned supply under this rule.
For z(p) = 100 − 10p, subtract the equilibrium price 10 from both sides. The price error evolves as e_next = (1 − 10λ)e. With λ = 0.05, each error is halved. Starting at 4 gives prices 7, 8.5 and 9.25. The path approaches 10 without crossing it.
With λ = 0.15, each error is multiplied by −0.5. Starting at 4 gives 13, 8.5 and 10.75. The path oscillates while approaching the same equilibrium. With λ = 0.25, errors are multiplied by −1.5 and grow in magnitude. The equilibrium equation has not changed; the adjustment behaviour has.
What a convergence plot can establish
A plot of the first path supports the statement that this particular update rule converges from this starting value in this model. It does not establish that actual traders use the rule or that actual prices follow the path. The coefficient λ requires a behavioural interpretation and appropriate units. It is not automatically a real-world speed of adjustment.
If this update rule is only a numerical algorithm, damping it changes the calculation method. If it is supposed to represent actual price-setting behaviour, damping it changes the economic model. The same line of code can have different meanings depending on which role it plays.
This distinction becomes crucial in policy discussions. A model can show a new equilibrium with higher output while omitting costly transitions, delayed responses or bankruptcies along the route. Report the equilibrium comparison as such. To make claims about transition costs, build and justify a model that includes them. A static answer is useful when its limits remain visible.
CHAPTER 6 OF 14 · Follow adjustment and decisions
6. Optimise choices while respecting constraints
Root finding asks where an equation is satisfied. Optimisation asks which feasible choice gives the greatest objective value. Sometimes an optimum satisfies a derivative equation, but solving that equation alone does not guarantee an optimum. Boundaries, discrete choices and multiple local optima must be considered.
Imagine an invented producer choosing daily output q between 0 and 12. Its net operating return is R(q) = 40q − 2q² − 50, in currency units per day. The derivative is 40 − 4q, giving the unconstrained candidate q = 10. The second derivative is −4, so this quadratic is strictly concave. The candidate lies within the feasible interval.
At q = 10, the return is 150. At q = 0, it is −50; at q = 12, it is 142. These evaluations confirm the candidate's meaning. If capacity is reduced to 8, the best feasible output becomes 8, giving 142. The unconstrained optimum remains a mathematical reference but is no longer implementable.
Make the action set explicit
Suppose instead output must be purchased in batches of three, so the feasible choices are 0, 3, 6, 9 and 12. Evaluating the objective gives the best choice q = 9 with return 148. Rounding 10 to the nearest integer would not respect the actual batch constraint. A solver must receive the correct action set.
Now ask whether shutdown avoids the fixed cost 50. The original formula assumes that cost is incurred even at zero output. If shutdown removes it, the model needs an additional choice with its own payoff. This is an economic specification issue, not a numerical rounding issue.
The Managerial Economics guide develops the interpretation of costs and decisions. A computational implementation should preserve those distinctions. Always report the objective's units, the feasible region, the chosen action and nearby alternatives. An output labelled simply “optimal” with no objective or constraints is incomplete.
CHAPTER 7 OF 14 · Follow adjustment and decisions
7. Let future consequences enter today's decision
A dynamic choice changes both the current payoff and the future state. Dynamic programming organises this problem by describing the state, feasible actions, immediate rewards and transition rules. The value of an action includes what it leaves available later, not only what it produces now.
Consider an original two-period equipment example. A machine starts in a worn state. In the final period, a worn machine earns 4 and a good machine earns 10. In the first period, using the worn machine earns 4 and leaves it worn. Repairing it costs 3, earns nothing immediately and makes it good for the final period. There is no uncertainty and the discount factor is 0.9.
Using now gives total discounted return 4 + 0.9 × 4 = 7.6. Repairing now gives −3 + 0.9 × 10 = 6. Repair is not optimal under these assumptions. A rule that always chooses the action with the better next-period machine would make the wrong decision because it ignores current cost and foregone output.
Change one condition and solve again
If repair costs only 1, its value becomes −1 + 0.9 × 10 = 8, exceeding 7.6. The threshold repair cost is 1.4: set −c + 9 equal to 7.6. This threshold is more informative than a single recommendation because it identifies the input capable of reversing the decision.
Work backwards from the final period, where no later consequences remain. Then use the calculated continuation values in the earlier comparison. QuantEcon's dynamic-programming material provides the broader framework for state-dependent decisions and discounted future rewards.
The example should not be extended without checking its horizon. A repair could be attractive over many periods even when it is unattractive over two. Salvage value, uncertain breakdowns, available repair capacity and the possibility of replacing the machine all change the action comparison. Computational convenience is not a reason to omit a consequence that determines the result.
CHAPTER 8 OF 14 · Compute distributions and approximations
8. Compute distributions rather than only averages
Economic models often track movement between states: employed and unemployed, low and high demand, or operating and failed equipment. A finite Markov model specifies probabilities of next-period states conditional on the present state. Its usefulness depends on whether the chosen state contains enough information for the intended question.
Take a fictional fixed population with two labour-market states. Each period, 2% of employed people become unemployed and 18% of unemployed people become employed. There is no population entry or exit. Let u be the unemployed share. The next share is u_next = 0.02(1 − u) + 0.82u = 0.02 + 0.80u.
If the initial share is 0.20, the next values are 0.18, 0.164 and 0.1512. A stationary share satisfies u = 0.02 + 0.80u, giving u = 0.10. At that distribution, expected flows into unemployment and out of unemployment are equal: 0.02 × 0.90 = 0.18 × 0.10 = 0.018 of the population.
Stationary does not mean motionless
People continue to move between states even though aggregate shares remain constant. In a population of 1,000 with the stationary proportions, expected inflows and outflows are both 18 people per period. The model does not say that the same 100 people remain unemployed forever.
QuantEcon's finite Markov-chain lecture explains transition matrices and stationary distributions. In a numerical implementation, each transition probability must be nonnegative and each row of a row-stochastic transition matrix must sum to one. A stationary distribution must also sum to one and reproduce itself under the transition operation.
The assumed transition rates are not real labour-market estimates. A policy that changes job finding may also change job separation or participation. Duration dependence could require separate states for short and long unemployment spells. Before using a computed stationary distribution as a forecast, ask whether the transition rules are stable and whether the real system has enough time to approach it.
CHAPTER 9 OF 14 · Compute distributions and approximations
9. Treat a grid as an approximation choice
A computer often replaces a continuous set of possible values with a finite grid. That choice controls what the model can represent. A coarse grid can miss a narrow peak, a binding constraint or a sharp change in a policy rule. Increasing the number of decimal places in the output does not repair a coarse state space.
Return to the producer with R(q) = 40q − 2q² − 50. Suppose an analyst tests only q = 0, 4, 8 and 12. The best observed return is 142, attained at both 8 and 12. The true continuous optimum is q = 10 with return 150. The grid therefore loses 8 currency units of return per day.
Refine the grid to include every two units. It now includes 10 and recovers the exact optimum in this particular quadratic example. That success is not a general proof that two-unit grids are sufficient. The relevant scale depends on the curvature of the objective, the constraints and the decision being made.
Compare the result that matters
A useful convergence table records grid resolution, chosen policy, objective value and computing cost. If the objective changes little while the policy changes substantially, inspect whether the objective is nearly flat. If the policy changes only at a threshold, inspect the grid around that threshold rather than refining every region equally.
Interpolation estimates values between stored grid points. It can improve efficiency, but it introduces assumptions about shape. Extrapolation beyond the grid is a further step and should be identified explicitly. A model that silently extrapolates household behaviour outside its income range may produce smooth but unsupported answers.
Grid checks should include boundaries. If many simulated agents accumulate at the maximum permitted asset value, the upper bound may be constraining the answer artificially. Expand the domain and compare. If the conclusion changes, report that dependence. The computational domain is part of the numerical specification, and its influence belongs in the evidence supporting the result.
CHAPTER 10 OF 14 · Compute distributions and approximations
10. Separate simulation noise from economic uncertainty
Simulation draws possible outcomes from a model. Repeating it helps describe the distribution implied by the assumed rules. More repetitions can reduce Monte Carlo noise, but they do not make unsupported transition probabilities or behavioural assumptions true.
Consider an invented household income shock. Income is 100 with probability 0.8 and 40 with probability 0.2. Expected income is 88. Expected squared deviation from that mean is 0.8 × 12² + 0.2 × 48² = 576, so the standard deviation is 24. For independent draws, the standard error of the sample mean is 24 divided by the square root of the number of draws.
With 100 independent draws, that standard error is 2.4. With 10,000, it is 0.24. Increasing the sample size one hundredfold reduces this measure of simulation noise tenfold. These are properties of the invented distribution, not estimates of household income uncertainty in any country.
Check dependence and the target statistic
If observations come from successive periods of a persistent process, independence may fail. The simple standard-error formula can then be misleading. Similarly, accurately estimating a mean does not ensure an accurate estimate of a rare loss probability. The simulation design must match the statistic that informs the decision.
Record the random-number method and seed for reproducibility, then test whether conclusions remain similar under independent seeds. Reusing one seed can make a calculation repeatable; it does not demonstrate that its output is representative. For comparisons between policies, carefully designed common random draws can reduce comparison noise, but the pairing and interpretation must be deliberate.
A useful report separates three questions. How much does the answer move because of random simulation draws? How much does it move when uncertain parameters change? How much does it move under a different plausible model structure? Those uncertainties have different causes and need different remedies. Running another million draws addresses only the first.
CHAPTER 11 OF 14 · Compare policies and diagnose errors
11. Re-solve the model when the policy changes
A counterfactual asks what the model implies under a different condition. It requires changing the relevant rule and solving the resulting system. Holding every behaviour fixed can be useful as an accounting exercise, but it is not the same as calculating a new equilibrium.
Return to demand D(p_b) = 120 − 4p_b and supply S(p_s) = 20 + 6p_s. Now introduce an invented per-unit charge of 5, with buyer price p_b = p_s + 5. Market clearing becomes 120 − 4(p_s + 5) = 20 + 6p_s. This gives seller price 8, buyer price 13 and quantity 68.
Before the charge, both prices were 10 and quantity was 80. Under the model, buyers pay 3 more per unit, sellers receive 2 less and traded quantity falls by 12. Charge revenue is 5 × 68 = 340 currency units per day. Multiplying 5 by the old quantity would instead give 400, because that calculation ignores the quantity response.
Interpret the comparison without adding claims
The split between buyer and seller prices follows the assumed demand and supply responses. It is not determined merely by which party formally sends the payment. The numerical result does not establish the actual incidence of a real charge without evidence supporting those curves and the institutional setting.
Revenue is also not the same as social benefit. A welfare analysis needs explicit treatment of gains, losses, external effects, administrative costs and the use of revenue. Different distributional weights can change an evaluation even when everyone agrees on the predicted quantities.
For a second exercise, reduce the charge to 2. The same equations give seller price 9.2, buyer price 11.2, quantity 75.2 and revenue 150.4. Recompute rather than scaling every result mechanically from the first scenario. This habit becomes especially important in nonlinear models, where thresholds, capacity limits or changes in participation can make proportional extrapolation unreliable.
CHAPTER 12 OF 14 · Compare policies and diagnose errors
12. Diagnose a convincing but wrong result
A smooth graph and a success message are not enough. Start with feasibility: are quantities within permitted bounds, probabilities nonnegative and budgets balanced? Then check equation residuals using the saved solution. Finally inspect whether the model answers the intended economic question.
Suppose a program reports price 9.99 in the original market. Demand is 80.04 and supply is 79.94, leaving excess demand 0.10. That may be adequate for one teaching exercise and inadequate for another application. The important point is to state the residual and its units rather than describe the answer as exact.
Three repairs for three different failures
If the program returns price 10 but computes demand 70, inspect the demand implementation or parameter mapping. The equilibrium value alone may have been hard-coded or produced by a different equation. Test the functions separately against the hand calculations before investigating more elaborate numerical methods.
If demand and supply match precisely but the model predicts implausible quantities at nearby prices, the problem may lie in the model specification or calibration. Tightening the solver tolerance will not repair a behavioural relationship outside its defensible range. Compare the model's implications with independent evidence and reconsider its domain.
If a policy result reverses when the grid changes from 50 to 100 points, investigate numerical resolution before presenting a substantive conclusion. If it reverses only when a poorly known parameter changes slightly, the appropriate conclusion may be that the decision is sensitive to that parameter. These failures require different explanations.
The Computational Social Science guide complements these checks with questions about social mechanisms, digital evidence and representation. An agent-based model can explore interactions that are difficult to express as a single equilibrium equation, but it still needs clearly specified rules and validation. Emergent behaviour in a simulation is evidence about the simulated rules; its relationship to actual people must be established separately.
CHAPTER 13 OF 14 · Transfer and continue learning
13. Transfer the method when the context changes
A changed-context exercise tests whether the learner understands the conditions behind a method. Take the original market, but cap supply at 60 units per day. Supply becomes the smaller of 20 + 6p and 60. Demand remains 120 − 4p. Is the old equilibrium price 10 still valid?
At price 10, demand is 80 but capped supply is 60, leaving excess demand 20. The old answer fails direct substitution. On the capacity-constrained branch, set 120 − 4p = 60, giving p = 15. The uncapped supply expression there is 110, so the capacity cap is indeed binding. The candidate is consistent with the branch used to derive it.
Add a price ceiling
Now impose a maximum legal price of 12 within this fictional exercise. At 12, planned demand is 72 and supply is 60. The equations do not yield a market-clearing price within the permitted range. A program must not report 15 as an implementable outcome, nor silently reduce demand to 60 without specifying who receives the available goods.
To continue, the model needs a rationing or allocation mechanism. A queue, lottery, priority rule or resale market would imply different experiences and possibly different behaviour. Numerical failure to find a feasible clearing price may be a meaningful model result rather than a software defect.
For an independent task, change capacity to 70 while retaining the ceiling of 12. At the ceiling, demand is 72 and supply is 70, so a shortage of 2 remains. Without the ceiling, clearing on the capped branch requires price 12.5. Check that uncapped supply exceeds 70 at that price before accepting the branch calculation.
The transfer lesson is practical: repeat the economic checks whenever conditions change. Do not assume that a method suitable for a smooth unconstrained model remains suitable after adding discontinuities or restrictions. Write down which original assumptions survive, which fail and what additional mechanism is needed to answer the new question.
CHAPTER 14 OF 14 · Transfer and continue learning
14. Build an independent learning and review routine
Begin with a model small enough to solve by hand. Implement its equations, test known inputs and verify that the computed answer matches the benchmark. Then change one assumption at a time. This sequence makes errors interpretable and connects programming skill to economic reasoning.
A student's first project could reproduce the market examples here in a spreadsheet or short program. A second could evaluate the producer's discrete action set. A third could compare the two-period repair decisions. For each project, submit the assumptions, equations, inputs, numerical method, checks and interpretation together. A screenshot of a final number is not a complete explanation.
Must I learn advanced programming first?
No. The early examples require arithmetic, elementary algebra and clear organisation. Programming becomes valuable as the state space, number of agents or repetitions grows. Learn arrays, functions and reproducible data handling alongside the economic model, rather than postponing all economic reasoning until a software course is finished.
Does convergence prove the model is correct?
No. Convergence concerns the behaviour of the numerical procedure under its conditions. Verification asks whether the implementation solves the specified problem. Validation asks whether the model is useful for its intended real-world purpose. A converged calculation can fail either of the latter checks.
Is computational economics the same as econometrics?
They overlap but have different emphases. Econometrics investigates economic relationships with data and statistical assumptions. Computational economics develops and applies algorithms for solving and exploring models. Estimation itself can require substantial computation, and model solutions can be inputs to estimation. Neither discipline makes the other's evidence requirements disappear.
How should a real-world result be communicated?
State the question and population, then explain the main mechanism. Give the result with meaningful units and a comparison. Separate numerical error from parameter and structural uncertainty. Show the checks most capable of revealing a mistake and identify the assumptions that could reverse the conclusion. Avoid presenting conditional model output as a guaranteed future outcome.
Where should I continue?
Use the linked QuantEcon lectures for zero finding, dynamic programming and Markov models, and the official SciPy documentation for the conditions of its numerical routine. Return to the Economics and Econometrics roots for economic interpretation and evidence. The Consumer Economics guide supplies additional examples of feasible household choices and constraints.
The final test is to hand the model to another reader. Can they reproduce a worked calculation, identify an inadmissible answer and explain what changes when an assumption changes? If they can, the computation has become a tool for understanding rather than a number that must be accepted on trust.