Tags: microeconomic theory, managerial economics, Texas A&M, linear equations, slope, derivatives, decision making, sensitivity analysis, satisficing, value maximization, behavioural economics
This section covers the foundational maths you need for managerial economics (rearranging linear equations, taking derivatives, interpreting slope) and introduces the core frameworks for managerial decision-making: the six-step process, profit maximisation as the firm's objective, and the main alternative objectives firms may pursue.
Slope of a line
The rate of change of the dependent variable with respect to the independent variable. Equivalently: rise over run, the change in y divided by the change in x, or the coefficient on the independent variable in a linear equation. All of these definitions are interchangeable.
Derivative
A rule for finding the rate of change of a non-linear function at any point. For a polynomial term ax^n, the derivative is nax^(n-1). Applied term by term.
Inverse demand function
The demand equation rewritten with price (P) on the left-hand side, e.g. P = mQd + b. Useful for reading off the price intercept and for deriving marginal revenue.
Model (in managerial economics)
A simplified description of a process, relationship, or other phenomenon. Models come in two main types: deterministic (outcomes follow with certainty) and probabilistic (outcomes involve uncertainty). They select key features for analysis and deliberately ignore less important ones, helping managers translate options into predicted outcomes.
Sensitivity analysis
The process of examining how an optimal decision changes when key economic assumptions or facts vary. Used by management to stress-test projections against changes in competitor pricing, sales volumes, cost structures, and so on.
Satisficing behaviour
A management approach where the firm targets a satisfactory level of performance against a benchmark, rather than striving for the absolute maximum. The term contrasts with full optimisation.
Value maximisation
The theory-of-the-firm objective stating that management's ultimate goal is to maximise the long-run value of the firm, not merely short-term profit.
Sales maximisation
An alternative firm objective where management aims to maximise revenue (often linked to compensation incentives), sometimes at the expense of profit.
Behavioural economics
The study of how real decision-makers deviate from the perfectly rational model. Key finding: decision-makers are prone to biases, mistakes, and cognitive pitfalls.
Benefit-cost analysis
The decision framework used primarily by public-sector managers (e.g. government planners), who weigh the social costs and benefits of a decision rather than private profit alone.
Given 6P + 5Q = 10, solve for P:
6P = -5Q + 10
P = (-5/6)Q + 10/6
P = (-5/6)Q + 5/3
The slope is -5/6 and the intercept is 5/3
For f(x) = 5x² + 6x + 3, apply the power rule term by term:
f'(x) = 10x + 6
Three rules to remember: the power rule (bring down the exponent, reduce it by one), the constant multiple rule, and the sum rule (differentiate term by term)
A line intersecting a curve at a point does not automatically tell you which is steeper. The line could cross the curve at a steeper angle or a flatter one. You need to see the actual intersection to compare slopes.
The slope of a tangent line to a curve at a point equals the derivative of the curve at that point.
Listing all possible profit outcomes is only practical when alternatives are few. As the number of choices increases, enumeration becomes increasingly costly.
Sensitivity analysis is the step where you ask: "What happens to my optimal decision if the underlying facts change?"
The standard theory says the firm should maximise its value (the present value of all future profits).
Three main alternative objectives exist:
Satisficing: aim for an acceptable benchmark rather than the absolute best
Sales maximisation: grow revenue, often because managerial pay is tied to sales targets
Social responsibility: satisfy customers, investors, society, the environment, and other stakeholders
All three alternatives may be pursued at the expense of profit.
A private-sector manager (e.g. Ann at a construction company) focuses on profit and firm value.
A public-sector manager (e.g. David in city planning) uses benefit-cost analysis, weighing social costs and benefits.
Revenue maximisation explains a firm that deliberately cuts price to grow market share, accepting lower profits.
Decision-makers are not perfectly rational; they face cognitive constraints.
They can learn from mistakes, but are prone to systematic biases and pitfalls.
They are not guided solely by monetary incentives, nor do they always act in a highly calculative manner.
Rearranging for slope-intercept form: aP + bQ = c → P = (-b/a)Q + c/a Slope = -b/a, intercept = c/a
Power rule for derivatives: If f(x) = ax^n, then f'(x) = nax^(n-1)
⚠️ "Slope of a line" questions may list several definitions (rise/run, Δy/Δx, coefficient on x). The answer is typically "all of the above" since they are all equivalent.
⚠️ A line intersecting a curve does not tell you which is steeper without more information. Do not assume the line is the tangent.
⚠️ Sensitivity analysis is about varying assumptions to see how the optimal decision shifts. It is not the same as benefit-cost analysis or opportunity-cost analysis.
⚠️ The satisficing model is about achieving a satisfactory benchmark, not about satisfying customers (despite the similar word).
⚠️ Value maximisation refers to long-run firm value, not short-term profit.
⚠️ Public managers use benefit-cost analysis; private managers focus on profit/value maximisation.
Q: What is the slope and intercept when you solve 6P + 5Q = 10 for P?
A: Slope = -5/6, intercept = 5/3.
Q: What is the derivative of 5x² + 6x + 3?
A: 10x + 6.
Q: If a line intersects a curve at a point, which is steeper at that point?
A: You cannot tell without more information. The line could be steeper or flatter than the curve at the intersection.
Q: What is sensitivity analysis used for?
A: To examine how an optimal decision is affected when key economic facts or assumptions vary.
Q: According to the satisficing model, what is the firm's goal?
A: To achieve a satisfactory level of performance against a benchmark, rather than maximising profit or value.
Q: According to the theory of the firm, what is management's ultimate objective?
A: To maximise the value of the firm.
Q: A coffee shop cuts its price to grow market share to 55%, knowing profits will fall. What explains this?
A: Revenue maximisation. The firm is prioritising sales growth over profit.
Q: What does behavioural economics show about decision-makers?
A: They are prone to biases, mistakes, and pitfalls. They are not perfectly rational.
Q: What is a model in managerial economics?
A: A simplified description of a process, relationship, or phenomenon. Models can be deterministic or probabilistic. They select key features for analysis and help managers translate options into predicted outcomes.
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