A function is a rule that assigns exactly one output to each input.
Business idea:
Notation examples:
In business context:
Exam tip: Always mention practical restrictions like Q ≥ 0 and P ≥ 0.
A linear function has the form:
Where:
Interpretation:
Example: y = 50x + 1000
Graph basics:
A demand function shows relationship between quantity demanded (Qd) and price (P).
A common linear demand form:
Meaning:
If Qd = 100 − 2P:
So demand curve can be plotted using (P, Qd) points.
Note: In economics, we often plot Q on x-axis and P on y-axis, but for functions either way is acceptable if labelled clearly.
A supply function shows relationship between quantity supplied (Qs) and price.
A common linear supply form:
Meaning:
If Qs = 20 + 3P:
Cost that does not change with output (within relevant range): rent, salaries.
Cost that changes with output: raw materials, direct labour.
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Business mathematics are mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis.
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A function is a rule that assigns exactly one output to each input.
Business idea:
Notation examples:
In business context:
Exam tip: Always mention practical restrictions like Q ≥ 0 and P ≥ 0.
A linear function has the form:
Where:
Interpretation:
Example: y = 50x + 1000
Graph basics:
A demand function shows relationship between quantity demanded (Qd) and price (P).
A common linear demand form:
Meaning:
If Qd = 100 − 2P:
So demand curve can be plotted using (P, Qd) points.
Note: In economics, we often plot Q on x-axis and P on y-axis, but for functions either way is acceptable if labelled clearly.
A supply function shows relationship between quantity supplied (Qs) and price.
A common linear supply form:
Meaning:
If Qs = 20 + 3P:
Cost that does not change with output (within relevant range): rent, salaries.
Cost that changes with output: raw materials, direct labour.
TC = FC + VC
A common linear cost function:
AC = TC/Q (for Q>0)
MC is the additional cost of producing one more unit. If TC is linear: TC = F + vQ, then MC = v (constant).
Exam note: Real cost curves are often U-shaped, but at basic level linear model is acceptable.
TR = P × Q
If P is constant, TR is a straight line through origin.
If price depends on quantity (demand function), e.g., P = a − bQ, then: TR = (a − bQ)Q = aQ − bQ^2 (a quadratic).
AR = TR/Q = P
MR is additional revenue from selling one more unit.
Profit: Π = TR − TC
If TC = F + vQ and TR = pQ (constant price p), then: Π(Q) = pQ − (F + vQ) = (p − v)Q − F
This is a straight line:
Break-even occurs when Π = 0. 0 = (p − v)Q − F Q = F/(p − v)
Let:
Step method for a straight line y = mx + c:
Table method (good for demand/supply): Pick 2–3 prices and compute quantities.
Example Qd = 100 − 2P:
Plot points and join with a straight line.
Common exam instruction: Always label axes and write the equation on the graph.
From this topic
When P = 10: Qd = 100 − 2(10) = 80. When P = 30: Qd = 100 − 2(30) = 40.
As price increases from 10 to 30, quantity demanded falls from 80 to 40, showing an inverse (negative) relationship between price and demand.
TC = 10,000 + 200Q. For Q = 150: TC = 10,000 + 200×150 = 10,000 + 30,000 = ₹40,000.
Fixed cost part = ₹10,000. Variable cost per unit = ₹200, so variable cost at Q=150 is ₹30,000.
Profit is Π = TR − TC.
If price is constant p, then TR = pQ. If total cost is TC = F + vQ (fixed cost F and variable cost per unit v), then: Π(Q) = pQ − (F + vQ) = (p − v)Q − F.
Break-even means Π = 0: 0 = (p − v)Q − F (p − v)Q = F Q = F/(p − v)
Here (p−v) is contribution per unit. So break-even units are fixed cost divided by contribution per unit.