CBSE Class 12 Economics Chapter 8: Revenue NCERT Solutions

Solution:

When the Total Revenue (TR) curve is a positively sloping straight line passing through the origin, the demand curve (or price line) is a horizontal line. This is because a positively sloping straight line TR from the origin indicates that the price per unit of the commodity remains constant at every level of output. Since the demand curve represents the price at each quantity, a constant price is depicted by a horizontal line. In this scenario, Average Revenue (AR) and Marginal Revenue (MR) are also constant and equal to the price, hence they also form horizontal lines coinciding with the demand curve.

Solution:

When the Total Revenue (TR) curve is a horizontal straight line, it signifies that the total revenue remains constant irrespective of the quantity sold. This occurs when the price per unit decreases as more units are sold, but the decrease in price is exactly offset by the increase in quantity sold, such that TR does not change. This situation corresponds to a demand curve that is a rectangular hyperbola, where the price elasticity of demand is unity ($Ed\; =\; 1$) at all levels of output. The price falls proportionally to the increase in quantity demanded, keeping TR constant.

Solution:

When the Total Revenue (TR) curve is a horizontal straight line, it implies that the price per unit remains constant regardless of the quantity sold. This is because the TR curve being horizontal means that as more units are sold, the price does not change. The demand curve, which represents the price at different quantities, will therefore be a horizontal line. This situation is characteristic of a perfectly competitive market where firms are price takers and can sell any quantity at the prevailing market price.

Solution:

The shape of the Marginal Revenue (MR) curve depends on the shape of the Total Revenue (TR) curve:

(i) When TR curve is a positively sloped straight line:

If the TR curve is a positively sloped straight line passing through the origin, it means that the price (and Average Revenue, AR) is constant at each level of output. In this case, the Marginal Revenue (MR) is also constant and equal to the price (AR). Therefore, the MR curve will be a horizontal straight line, coinciding with the AR curve and the demand curve.

(ii) When TR curve is a horizontal straight line:

If the TR curve is a horizontal straight line, it implies that the total revenue does not change with an increase in the quantity sold. This happens when the price elasticity of demand is unity. In this scenario, the Marginal Revenue (MR) is zero for every unit sold, as the additional revenue gained from selling one more unit is zero. Consequently, the MR curve coincides with the x-axis.

Solution:

We are given the quantity sold and the Marginal Revenue (MR) at each level of output. We need to calculate Total Revenue (TR), the demand curve (which implies finding the price or Average Revenue, AR), and the price elasticity of demand.

1. Calculation of Total Revenue (TR):

Total Revenue is the cumulative sum of Marginal Revenue. TR = $\backslash sum\; MR$

Quantity | MR | TR ($\backslash sum\; MR$)

------- | -------- | --------

1 | 10 | 10

2 | 6 | 10 + 6 = 16

3 | 2 | 16 + 2 = 18

4 | 2 | 18 + 2 = 20

5 | 2 | 20 + 2 = 22

6 | 0 | 22 + 0 = 22

7 | 0 | 22 + 0 = 22

8 | 0 | 22 + 0 = 22

9 | -5 | 22 + (-5) = 17

2. Calculation of Demand Curve (Price or Average Revenue, AR):

Average Revenue (AR) is calculated as Total Revenue divided by Quantity (AR = TR / Q). The demand curve is represented by the AR values.

Quantity | TR | AR (TR/Q)

------- | -------- | --------

1 | 10 | 10 / 1 = 10

2 | 16 | 16 / 2 = 8

3 | 18 | 18 / 3 = 6

4 | 20 | 20 / 4 = 5

5 | 22 | 22 / 5 = 4.4

6 | 22 | 22 / 6 = 3.67 (approx.)

7 | 22 | 22 / 7 = 3.14 (approx.)

8 | 22 | 22 / 8 = 2.75

9 | 17 | 17 / 9 = 1.89 (approx.)

The demand curve is represented by these AR values at each quantity. For example, at Q=1, P=10; at Q=2, P=8; at Q=4, P=5.

3. Calculation of Price Elasticity of Demand (Ed):

The price elasticity of demand can be calculated using the formula $Ed\; =\; \backslash frac\{\backslash \%\backslash Delta\; Q\}\{\backslash \%\backslash Delta\; P\}$ or by using the relationship between MR and AR: $Ed\; =\; \backslash frac\{AR\}\{AR\; -\; MR\}$.

Let's calculate Ed at different points:

At Q=1: AR = 10, MR = 10. $Ed\; =\; \backslash frac\{10\}\{10\; -\; 10\}\; =\; \backslash frac\{10\}\{0\}$ (Undefined, which corresponds to $\backslash infty$ for the first unit when price is constant).

At Q=2: AR = 8, MR = 6. $Ed\; =\; \backslash frac\{8\}\{8\; -\; 6\}\; =\; \backslash frac\{8\}\{2\}\; =\; 4$.

At Q=3: AR = 6, MR = 2. $Ed\; =\; \backslash frac\{6\}\{6\; -\; 2\}\; =\; \backslash frac\{6\}\{4\}\; =\; 1.5$.

At Q=4: AR = 5, MR = 2. $Ed\; =\; \backslash frac\{5\}\{5\; -\; 2\}\; =\; \backslash frac\{5\}\{3\}\; =\; 1.67$ (Note: There seems to be an inconsistency in MR values provided for Q=3 and Q=4, as MR should generally decrease or stay constant, and AR decreases. If MR=2 for Q=3, AR=6, then for Q=4, if MR=2, AR should be 5. The elasticity calculation for Q=4 using AR=5 and MR=2 gives 5/3. Let's re-evaluate based on the provided MR values.)

Let's use the provided AR and MR values directly:

At Q=1: AR=10, MR=10. $Ed\; =\; \backslash frac\{10\}\{10-10\}$ (Undefined, implies $\backslash infty$)

At Q=2: AR=8, MR=6. $Ed\; =\; \backslash frac\{8\}\{8-6\}\; =\; \backslash frac\{8\}\{2\}\; =\; 4$

At Q=3: AR=6, MR=2. $Ed\; =\; \backslash frac\{6\}\{6-2\}\; =\; \backslash frac\{6\}\{4\}\; =\; 1.5$

At Q=4: AR=5, MR=2. $Ed\; =\; \backslash frac\{5\}\{5-2\}\; =\; \backslash frac\{5\}\{3\}\; \backslash approx\; 1.67$

At Q=5: AR=4.4, MR=2. $Ed\; =\; \backslash frac\{4.4\}\{4.4-2\}\; =\; \backslash frac\{4.4\}\{2.4\}\; \backslash approx\; 1.83$

At Q=6: AR=3.67, MR=0. $Ed\; =\; \backslash frac\{3.67\}\{3.67-0\}\; =\; 1$

At Q=7: AR=3.14, MR=0. $Ed\; =\; \backslash frac\{3.14\}\{3.14-0\}\; =\; 1$

At Q=8: AR=2.75, MR=0. $Ed\; =\; \backslash frac\{2.75\}\{2.75-0\}\; =\; 1$

At Q=9: AR=1.89, MR=-5. $Ed\; =\; \backslash frac\{1.89\}\{1.89\; -\; (-5)\}\; =\; \backslash frac\{1.89\}\{6.89\}\; \backslash approx\; 0.27$

Summary:

Total Revenue (TR) Schedule: 10, 16, 18, 20, 22, 22, 22, 22, 17 for quantities 1 through 9.

Demand Curve (AR values): 10, 8, 6, 5, 4.4, 3.67, 3.14, 2.75, 1.89 for quantities 1 through 9.

Price Elasticity of Demand (Ed): Varies from $\backslash infty$ to 0.27, with values of 4, 1.5, 1.67, 1.83, 1, 1, 1, 0.27 at different quantities.