Functions and Graphs for Business: Cost, Revenue, Profit, Demand and Supply (Basics) Questions

Question 1

Define a function.

Accepted Answer

A function is a rule that assigns exactly one output to each input.

Question 2

What is domain of a function?

Accepted Answer

Domain is the set of permissible input values for a function.

Question 3

Write the formula of total revenue.

Accepted Answer

Total revenue TR = Price × Quantity (TR = P×Q).

Question 4

Define fixed cost.

Accepted Answer

Fixed cost is cost that does not change with output (within relevant range).

Question 5

What is profit?

Accepted Answer

Profit is the excess of total revenue over total cost (Π = TR − TC).

Question 6

State break-even condition.

Accepted Answer

Break-even occurs when total revenue equals total cost (TR = TC).

Question 7

Given Qd = 100 − 2P, find Qd when P = 10 and when P = 30. Comment on relationship.

Accepted Answer

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.

Question 8

Given TC = 10,000 + 200Q, find TC for Q = 150 and identify fixed and variable parts.

Accepted Answer

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.

Question 9

Find equilibrium price and quantity when Qd = 100 − 2P and Qs = 20 + 3P.

Accepted Answer

Equilibrium occurs where quantity demanded equals quantity supplied.

Given:
Qd = 100 − 2P
Qs = 20 + 3P

At equilibrium: Qd = Qs
100 − 2P = 20 + 3P
100 − 20 = 5P
80 = 5P
P = 16

Now substitute P = 16 into either equation:
Q = 100 − 2(16) = 100 − 32 = 68

So equilibrium price is ₹16 and equilibrium quantity is 68 units.

Question 10

Explain how to draw a straight-line graph for y = mx + c in an exam.

Accepted Answer

1) Find intercept: when x = 0, y = c, so plot (0, c).
2) Choose a convenient x (like 10), compute y = m(10) + c and plot second point.
3) Join the two points to get a straight line.
4) Label axes clearly and write the equation on the graph.

Question 11

Explain the meaning of TR, AR and MR (basic).

Accepted Answer

Total Revenue (TR), Average Revenue (AR) and Marginal Revenue (MR) are key revenue concepts.

- TR is the total sales value: TR = P × Q.
- AR is revenue per unit sold: AR = TR/Q. In basic price-taking case, AR equals price (AR = P).
- MR is additional revenue from selling one more unit.

If price is constant, each extra unit adds the same revenue, so MR = P.
If price falls with more output (downward sloping demand), then MR is less than price because to sell extra units, price must be reduced.

These concepts are used to analyze pricing, output decisions and profit planning.

Question 12

A firm sells at ₹500, variable cost ₹300, fixed cost ₹40,000. Find break-even units.

Accepted Answer

Contribution per unit = 500 − 300 = ₹200.
Break-even units = Fixed cost / contribution = 40,000/200 = 200 units.

So, the firm must sell 200 units to break even.

Question 13

Derive the break-even quantity formula using TR and TC and explain the meaning of contribution.

Accepted Answer

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.

Question 14

Explain demand and supply functions and show how equilibrium is determined with a numerical example.

Accepted Answer

Demand function shows how quantity demanded depends on price, usually with negative relation (e.g., Qd = a − bP). Supply function shows how quantity supplied depends on price, usually with positive relation (e.g., Qs = c + dP).

Equilibrium is where Qd = Qs.
Example: Qd = 100 − 2P, Qs = 20 + 3P.
Set equal: 100 − 2P = 20 + 3P ⇒ 80 = 5P ⇒ P = 16.
Then Q = 100 − 2(16) = 68.

So equilibrium price is 16 and equilibrium quantity is 68. This point balances market demand and supply.

Question 15

Given TC = 10,000 + 200Q and price p = 400 per unit, form TR and profit function and find break-even output.

Accepted Answer

Given:
TC = 10,000 + 200Q
Price p = 400 per unit

1) Total Revenue:
TR = pQ = 400Q

2) Profit function:
Π = TR − TC
= 400Q − (10,000 + 200Q)
= 200Q − 10,000

3) Break-even:
Set Π = 0
200Q − 10,000 = 0
200Q = 10,000
Q = 50 units

Interpretation: The firm must sell 50 units to cover fixed cost and start earning profit.

Functions and Graphs for Business: Cost, Revenue, Profit, Demand and Supply (Basics)

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