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Published on: 27/09/2019
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Questions + Answers key
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1.
What is the relationship between TR and Price line when price is constant?
2.
The demand function of a commodity x is Qx = 12 - Px (where Qx = the quantity demanded of a commodity x and Px = price of the commodity x). Derive the TR and MR schedules when the price of commodity varies from Rs 12 to Rs 1.
3.
Database of Maruti-Suzuki Co. got damaged in an accidental fire. The management attempted to imagine data. The following table emerged after brainstorming sessions between company executives and consultants. Is this data correct?
| AR | TR |
| 10 | 100 |
| 12 | 130 |
| 15 | 300 |
| 20 | 500 |
4.
Calculate TR, AR and MR from the following data.
| Price(Rs) | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| units sold | 100 | 90 | 80 | 70 | 60 | 50 | 40 |
5.
Explain the relation between marginal revenue and average revenue when a firm is able to sell more quantity of output: (i) at the same price. (ii) only by lowering the price.
6.
A seller sells 3 diamond rings of Rs 15000 each. If a seller sells his 4th diamond ring, his MR becomes Rs 13500. Calculate the price at which the seller sells his fourth ring.
7.
Calculate TR, AR and MR.
| Units sold | 6 | 7 | 8 |
| Price(Rs) | 5 | 4 | 3 |
8.
Complete the following table.
| Output (units) | 1 | 2 | 3 | 4 |
| Price (Rs) | - | 9 | - | - |
| TR(Rs) | - | - | 24 | - |
| MR(Rs) | 10 | - | - | 4 |
9.
Complete the following table.
| Units sold | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| TR(Rs) | 20 | - | 48 | - | 60 | 60 | 56 | - |
| MR(Rs) | 20 | - | - | 8 | - | 0 | - | -8 |
| AR(Rs) | - | 18 | - | 14 | 12 | - | 8 | 6 |
10.
Complete the following table.
| Price(Rs) | 10 | 9 | 6 | 4 |
|---|---|---|---|---|
| Output (units) | 1 | 2 | 3 | 4 |
| TR(Rs) | - | - | - | - |
| MR(Rs) | - | - | - | - |
11.
Complete the following table.
| Price(Rs) | 12 | 10 | 8 | 6 |
|---|---|---|---|---|
| Output (units) | 1 | 2 | 3 | 4 |
| TR(Rs) | - | - | - | - |
| MR(Rs) | - | - | - | - |
12.
Calculate TR and MR from the following data.
| units sold | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| AR(Rs) | 25 | 23 | 21 | 19 | 18 | 15 |
13.
Comment on the shape of the MR curve in case the TR curve is a
(i) positively sloped straight line,
(ii) horizontal straight line.
14.
Whatwouldbetheshapeofthe demand curve so that the total revenue curve is
(a) A positively sloped straight line passing through the origin?
(b) A horizontal line?
15.
Compute the total revenue, marginal revenue and average revenue schedules in following table. Market price of each unit of goods is Rs 10.
| Quantity sold | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| TR(Rs) | |||||||
| AR(Rs) | |||||||
| MR(Rs) |
1.
When price of a commodity is constant, Price = AR = MR at all levels of output. Therefore, price line is the same as MR curve. Also, TR = ΣMR. So, the area under MR curve or price line will be equal to TR. In Figure, TR at OQ level of output = OP x OQ = Area under price line.
2.
| Price(Rs) | units sold | TR(Rs)=PxQ | MR(Rs)MRn=TRn-TRn-1 |
|---|---|---|---|
| 12 | 0 | 0 | - |
| 11 | 1 | 11 | 11 |
| 10 | 2 | 20 | 9 |
| 9 | 3 | 27 | 7 |
| 8 | 4 | 32 | 5 |
| 7 | 5 | 35 | 3 |
| 6 | 6 | 36 | 1 |
| 5 | 7 | 35 | -1 |
| 4 | 8 | 32 | -3 |
| 3 | 9 | 27 | -5 |
| 2 | 10 | 20 | -7 |
| 1 | 11 | 11 | -9 |
Note: Putting the various values of price from Rs 12 to Rs 1 in Q = 12 - Px, we get the corresponding values of the quantities demanded (For example, Qx will be 0 when Px = 12).
3.
The data presented by the company is seriously flawed. It indicates that as the company raises the price of its product, it is in a position to sell more. This is contrary to the assumption of law of demand which holds that there is inverse relationship between the price of a commodity and its quantity demanded.
Value: Analytic
4.
| Price(Rs)(P) | units sold(Q) | TR(Rs)=PxQ | \(AR(Rs)=\frac{TR}{Q}\) | \(MR(Rs)\frac{\triangle TR}{\triangle Q}\) |
| 1 | 100 | 100 | 1 | -8 |
| 2 | 90 | 180 | 2 | -6 |
| 3 | 80 | 240 | 3 | -4 |
| 4 | 70 | 280 | 4 | -2 |
| 5 | 60 | 300 | 5 | 0 |
| 6 | 50 | 300 | 6 | 2 |
| 7 | 40 | 280 | 7 | - |
(i) MR has been calculated m the reverse order, i.e., from bottom to top.
(ii) MR has been calculated after dividing the change in TR by 10 units (as units sold are given at the gap of 10 units).
5.
(i) Relationship between Average Revenue and Marginal Revenue at a same price
(a) When price remains the same at all output levels, the firm cannot influence the prevailing market price of the commodity. The price is given to it.
(b) It can sell any amount of the commodity at this given price. Under such a case firm's average and marginal revenue remains equal and their curves coincide as shown in given figure.
(ii) Relationship between Average Revenue and Marginal Revenue by lowering the price
(a) When price falls, with rise in output, then AR falls, MR also falls but at a much faster rate. As a result, the revenue from every additional unit (i.e.MR) will be less than AR.
(b) As a result, both AR and MR curves slope downwards from left to right. This can be explained with the help of given Figure.
6.
TR of 3 diamond ring = Rs 15,000 x 3 = Rs 45,000
MR of 4th diamond ring = Rs13,500
TR of 4 diamond ring = Rs 45,000 + 13,500 = Rs 58,500
Price (AR)of 4th diamond ring = TR of 4th diamond ring ÷ 4
AR = Rs 14,625
Price of 4th diamond ring = Rs 14,625.
7.
| Units sold(Q) | Price(Rs)(P) | TR(Rs)=PxQ | \(AR(Rs)=\frac{TR}{Q}\) | MR(Rs)MRn=TRn-TRn-1 |
|---|---|---|---|---|
| 6 | 5 | 30 | 5 | - |
| 7 | 4 | 28 | 4 | -2 |
| 8 | 3 | 24 | 3 | -4 |
8.
| Output (units) | Price | TR | MR |
|---|---|---|---|
| 1 | \(10[\frac{TR}{Q}]\) | 10[MR of unit 1] | 10 |
| 2 | 9 | 18[PxQ] | \(8[\frac{\triangle TR}{\triangle Q}]\) |
| 3 | \(8[\frac{TR}{Q}]\) | 24 | \(6[\frac{\triangle TR}{\triangle Q}]\) |
| 4 | \(7[\frac{TR}{Q}]\) | 28[24+4] | 4 |
9.
| (Q) | TR | MR | AR |
|---|---|---|---|
| 1 | 20 | 20 | \(20[\frac{TR}{Q}]\) |
| 2 | 36[ARxQ] | \(16[\frac{\triangle TR}{\triangle Q}]\) | 18 |
| 3 | 48 | \(12[\frac{\triangle TR}{\triangle Q}]\) | \(16[\frac{TR}{Q}]\) |
| 4 | 56[48+8] | 8 | 14 |
| 5 | 60 | \(4[\frac{\triangle TR}{\triangle Q}]\) | 12 |
| 6 | 60 | 0 | \(10[\frac{TR}{Q}]\) |
| 7 | 56 | \(-4[\frac{\triangle TR}{\triangle Q}]\) | 8 |
| 8 | 48[56-8] | -8 | 6 |
10.
| Price(P)(Rs) | Output (units) | TR(Rs)=P x Q | MR(Rs)MRn=TRn-TRn-1 |
|---|---|---|---|
| 10 | 1 | 10 | 10 |
| 9 | 2 | 18 | 8 |
| 6 | 3 | 18 | 0 |
| 4 | 4 | 16 | -2 |
11.
| Price (P)(Rs) | Output (Units) | TR(Rs)=PxQ | MR(Rs) TRn-TRn-1=MRn |
|---|---|---|---|
| 12 | 1 | 12 | 12 |
| 10 | 2 | 20 | 8 |
| 8 | 3 | 24 | 4 |
| 6 | 4 | 24 | 0 |
12.
| Units sold (Q) | AR(Rs) | TR(Rs)=PxQ | MR(Rs)=TRn-TRn-1=MRn |
|---|---|---|---|
| 1 | 25 | 25 | 25 |
| 2 | 23 | 46 | 21 |
| 3 | 21 | 63 | 17 |
| 4 | 19 | 76 | 13 |
| 5 | 18 | 90 | 14 |
| 6 | 15 | 90 | 0 |
13.
(i) When TR curve is positively sloped straight line, MR is a horizontal line. MR coincides with the demand curve. Price or AR is constant at each level of output.
When AR is constant, MR is also constant.
(ii) When TR is a horizontal straight line, MR is zero. It is because horizontal TR means when price falls, quantity demanded rises in the same proportion. Thus, MR is zero. MR curve coincides with the x-axis.
14.
(a) When TR curve is a positively sloping straight line passing through the origin, demand curve (or price line) will be horizontal. It is shown in the shown in the reason is that demand curve is also the price line. When TR is a straight positively sloped line, price at each level of output is constant.
(b) When TR is a horizontal line, demand curve is a rectangular hyperbola. It is shown:
The reason is that, the price at each level of output declines.
15.
| (P) | (Q) | TR=PxQ | AR(Price)= | MRn=TRn-TRn-1 |
| 10 | 0 | 0 | - | - |
| 10 | 1 | 10 | 10 | 10 |
| 10 | 2 | 20 | 10 | 10 |
| 10 | 3 | 30 | 10 | 10 |
| 10 | 4 | 40 | 10 | 10 |
| 10 | 5 | 50 | 10 | 10 |
| 10 | 6 | 60 | 10 | 10 |
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