The market demand curve for a commodity and the total cost for a monopoly firm producing the commodity is given by the schedules below. Use the information to calculate the following:

(a) The MR and MC schedules
(b) The quantites for which the MR and MC are equal
(c) The equilib

Question

The market demand curve for a commodity and the total cost for a monopoly firm producing the commodity is given by the schedules below. Use the information to calculate the following:

(a) The MR and MC schedules
(b) The quantites for which the MR and MC are equal
(c) The equilibrium quantity of output and the equilibrium price of the commodity
(d) The total revenue, total cost and total profit in equilibrium.

| Quantity | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Price | 52 | 44 | 37 | 31 | 26 | 22 | 19 | 16 | 13 |
| Total Cost | 10 | 60 | 90 | 100 | 102 | 105 | 109 | 115 | 125 |

Accepted Answer

> [!TLDR]
> $MR = MC$ at $q = 2$ and $q = 6$; equilibrium is $q = 6$ (where $MC$ is rising), price Rs 19, $TR = 114$, $TC = 109$, profit $= 	ext{Rs }5$.

**(a) The $MR$ and $MC$ schedules.** First find total revenue $TR = P 	imes q$, then $MR = \Delta TR$ and $MC = \Delta TC$:

| $q$ | $P$ | $TR = P	imes q$ | $MR = \Delta TR$ | $TC$ | $MC = \Delta TC$ |
| --- | --- | --- | --- | --- | --- |
| 0 | 52 | 0 | – | 10 | – |
| 1 | 44 | 44 | 44 | 60 | 50 |
| 2 | 37 | 74 | 30 | 90 | 30 |
| 3 | 31 | 93 | 19 | 100 | 10 |
| 4 | 26 | 104 | 11 | 102 | 2 |
| 5 | 22 | 110 | 6 | 105 | 3 |
| 6 | 19 | 114 | 4 | 109 | 4 |
| 7 | 16 | 112 | -2 | 115 | 6 |
| 8 | 13 | 104 | -8 | 125 | 10 |

**(b) Quantities where $MR = MC$.** Comparing the two columns, $MR = MC$ at **$q = 2$** (both 30) and at **$q = 6$** (both 4). …

$q$	$P$	$TR = P\times q$	$MR = \Delta TR$	$TC$	$MC = \Delta TC$
0	52	0	–	10	–
1	44	44	44	60	50
2	37	74	30	90	30
3	31	93	19	100	10
4	26	104	11	102	2
5	22	110	6	105	3
6	19	114	4	109	4
7	16	112	-2	115	6
8	13	104	-8	125	10

$q$	$P$	$TR = P\times q$	$MR = \Delta TR$	$TC$	$MC = \Delta TC$
0	52	0	–	10	–
1	44	44	44	60	50
2	37	74	30	90	30
3	31	93	19	100	10
4	26	104	11	102	2
5	22	110	6	105	3
6	19	114	4	109	4
7	16	112	-2	115	6
8	13	104	-8	125	10

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$q$	$P$	$TR = P\times q$	$MR = \Delta TR$	$TC$	$MC = \Delta TC$
0	52	0	–	10	–
1	44	44	44	60	50
2	37	74	30	90	30
3	31	93	19	100	10
4	26	104	11	102	2
5	22	110	6	105	3
6	19	114	4	109	4
7	16	112	-2	115	6
8	13	104	-8	125	10