Importance and Use of Mathematics in Economics
Economics uses **mathematics and statistics** as quantitative tools to express relationships precisely, analyse data, and solve problems. **Basic mathematics** (addition, subtraction, multiplication, division) is the foundation; on top of it sit **arithmetic, geometry, algebra, and calculus**. Mathematics helps economists (1) study cause-effect relationships, (2) analyse three or more values, (3) convert sentences into symbols, (4) express economic phenomena algebraically, (5) find slopes of curves, (6) study marginal and total concepts, and (7) solve linear and non-linear programming problems. Key equations include the linear demand function Qd = a − bP, the slope formula m = Δy/Δx, and the marginal cost definition MC = dTC/dQ.
In this chapter
Quantitative Technique in Economics
Economics is partly quantitative — it measures things like price, quantity, income, GDP, inflation rate. To handle these measurements precisely, economists use mathematics and statistics as tools. This is called the quantitative technique in economics. Basic mathematics includes the four operations — addition (+), subtraction (−), multiplication (×), division (÷) — that every student learns in primary school. On this foundation sit four higher branches: arithmetic (numbers and their properties), geometry (shapes and graphs), algebra (symbols and equations), and calculus (rates of change). Economics uses all of these, especially algebra and calculus.
Foundation of Mathematics for Economics
- Basic mathematics — addition, subtraction, multiplication, division (+, −, ×, ÷).
- Arithmetic — study of numbers, ratios, percentages (e.g. inflation rate 7.9%).
- Geometry — shapes and graphs (e.g. demand curve, supply curve, PPF).
- Algebra — symbols and equations (e.g. Qd = 100 − 2P; solve for P).
- Calculus — rates of change (e.g. marginal cost MC = dTC/dQ).
- These five branches together form the mathematical foundation for economic analysis.
Importance and Uses of Mathematics in Economics
Uses of Mathematics in Economics
| Use | Explanation | Example |
|---|---|---|
| 1. Study cause-effect relationship | Show how one variable affects another | Price ↑ → demand ↓ (law of demand) |
| 2. Analyse 3 or more values | Compare many goods/years/consumers at once | Demand for rice, wheat, maize in same year |
| 3. Convert sentences into symbols | Replace words with letters for brevity | "Quantity demanded of rice" → Qd_rice |
| 4. Express phenomena algebraically | Write economic laws as equations | Qd = a − bP (linear demand) |
| 5. Find slope of curves | Measure rate of change between two variables | Slope of demand curve = ΔQd/ΔP |
| 6. Study marginal & total concepts | Use derivatives for marginal; integrals for total | MC = dTC/dQ; TC = ∫MC dQ |
| 7. Linear & non-linear programming | Optimise (max profit / min cost) under constraints | Maximise output of a factory given budget |
Key Equations in Mathematical Economics
Linear demand function (Qd = quantity demanded, P = price, a = autonomous demand, b = price sensitivity)
Slope of a line (rate of change of y with respect to x)
Marginal cost & marginal revenue (derivative of total cost / total revenue with respect to quantity)
These three equations are the backbone of mathematical economics in Class 11. The demand function Qd = a − bP shows how quantity demanded falls as price rises (b > 0). The slope formula m = Δy/Δx measures the steepness of any line — for a demand curve, slope = ΔQd/ΔP, which is negative (showing inverse relationship). The marginal cost MC = dTC/dQ uses calculus (derivative of total cost) to show how much cost rises when one extra unit is produced — for example, the cost of producing the 6th plate of momos at a New Road restaurant.
Math in Daily Nepali Economics
Mathematics is everywhere in Nepali economic life. When you calculate the demand for rice in Kathmandu (Qd = 1000 − 50P, where P is Rs/kg), you use algebra. When the cost of producing momos at a New Road stall rises from Rs 30 to Rs 35 as the 50th plate is added, the marginal cost is ΔTC/ΔQ = (35-30)/(50-49) = Rs 5 — that's calculus. When a shopkeeper in Asan compares prices of 5 types of cooking oil, that's analysing 3+ values. The slope of demand for salt is shallow (salt is a necessity), while the slope of demand for restaurant meals is steep. Mathematics makes economics precise and powerful.
Practice Problem
The demand for rice in Kathmandu is given by Qd = 1200 − 40P and the supply by Qs = 200 + 20P, where P is in Rs per kg and Q in kg per day. (a) Find the equilibrium price P and quantity Q. (b) Find the slope of the demand curve. (c) What happens if the government fixes a price ceiling of Rs 15/kg — calculate shortage.
Practice Problem
A momo stall in New Road, Kathmandu has the following total cost (TC) data for producing plates of momos: TC(50 plates) = Rs 1500, TC(51 plates) = Rs 1525, TC(52 plates) = Rs 1560. (a) Calculate the marginal cost (MC) of the 51st plate. (b) Calculate the marginal cost of the 52nd plate. (c) If each plate sells for Rs 35, should the stall produce the 52nd plate? Explain.
Quick Revision
- Mathematics + statistics = quantitative tools of economics.
- Basic math = +, −, ×, ÷; foundation for arithmetic, geometry, algebra, calculus.
- 7 uses: cause-effect, 3+ values, symbols, algebra, slope, marginal/total, programming.
- Linear demand: Qd = a − bP (b > 0); slope = ΔQd/ΔP = −b.
- Slope formula: m = Δy/Δx = (y₂ − y₁)/(x₂ − x₁).
- Marginal cost: MC = dTC/dQ ≈ ΔTC/ΔQ; marginal revenue: MR = dTR/dQ.
- Equilibrium: set Qd = Qs, solve for P, then back-substitute for Q.
- Profit-max rule: produce where MC = MR (price in perfect competition).
- Math makes economics precise — demand for rice in Kathmandu, cost of momos in New Road.