Chapter 2: Market and Revenue Curves

Monopoly is the market structure where there is a single seller. The monopoly firm is a price maker. To increase sales, it must reduce price. Therefore, both AR and MR curves slope downward. MR decreases faster than AR. AR is never zero, but MR can be zero or negative. Understanding these Market and Revenue Curves is crucial for monopoly analysis.

In the figure, AR and MR are downward sloping. MR is less than AR at all levels of output.

Market: A mechanism where buyers and sellers interact to exchange goods/services.
Structures:
i. Perfect Competition: Many buyers/sellers, homogeneous product, price taker.
ii. Monopoly: Single seller, no close substitutes, price maker.
iii. Imperfect Competition: Reality between the two extremes (e.g., Monopolistic competition, Oligopoly).

Perfect competition is a market structure with a large number of buyers and sellers with a homogeneous product. The firm is a ‘price-taker’.

Observation: Price (AR) is constant at Rs. 10. TR increases at a constant rate. MR is also constant and equal to AR. Thus: AR = MR = P.

Under monopoly, MR slopes downward because the firm must lower prices to sell more units. The MR curve lies below the AR curve. It intersects the X-axis when TR is maximum (MR=0) and goes below the X-axis (negative) when TR declines.

In perfect competition, the firm sells homogeneous products at a uniform price. The firm does not have to reduce the price to sell more. Thus, AR is constant. Since AR is constant, MR is also constant and equal to AR. The Market and Revenue Curves are horizontal straight lines parallel to the X-axis.

Under monopoly, the firm is a price maker. To sell more, price must be lowered. TR increases at a decreasing rate initially, reaches a maximum, and then falls.

Please refer to the answer for Question 9 (Relationship among TR, MR, and AR in perfect competition). The derivation is identical.

Please refer to the answer for Question 12 (Derivation of AR and MR from TR under monopoly market).

Solution:

Given TR = 5Q – 3Q² + 2Q³

Step 1: Find AR Function
AR = TR / Q = (5Q – 3Q² + 2Q³) / Q = 5 – 3Q + 2Q²

Step 2: Find MR Function
MR = d(TR)/dQ = d(5Q – 3Q² + 2Q³)/dQ = 5 – 6Q + 6Q²

Step 3: Calculate at Q=5
AR = 5 – 3(5) + 2(5)² = 5 – 15 + 50 = 40
MR = 5 – 6(5) + 6(5)² = 5 – 30 + 150 = 125

Answer: AR = Rs. 40, MR = Rs. 125

Solution:

Given TR = 100Q – 4Q²

Step 1: AR
AR = TR/Q = (100Q – 4Q²) / Q = 100 – 4Q
At Q=2: AR = 100 – 4(2) = 100 – 8 = 92

Step 2: MR
MR = d(TR)/dQ = 100 – 8Q
At Q=2: MR = 100 – 8(2) = 100 – 16 = 84

Answer: AR = Rs. 92, MR = Rs. 84

Solution:

Given AR = 20 – 4Q

Step 1: Find TR
TR = AR × Q = (20 – 4Q) × Q = 20Q – 4Q²
At Q=2: TR = 20(2) – 4(2)² = 40 – 16 = 24

Step 2: Find MR
MR = d(TR)/dQ = 20 – 8Q
At Q=2: MR = 20 – 8(2) = 20 – 16 = 4

Answer: TR = Rs. 24, MR = Rs. 4