Question

The table shows the Hornet nation’s demand for stingers. The marginal cost of stingers for each seller is $10. If there are six sellers of stingers in Hornet and if they collude, then what will be the price and quantity of each seller?

Quantity	Price	Total Revenue
0	$20	$0
10	$18	$180
20	$16	$320
30	$14	$420
40	$12	$480
50	$10	$500
60	$8	$480
70	$6	$420
80	$4	$320
90	$2	$180
100	$0	$0

Answer 1

In order to maximize profit a firm produces that quantity at which MR = MC

where MC = marginal cost and MR = Marginal revenue.

Here six firms collude and hence will work together and produce that quantity at which MR = MC

Here, MC = 10

MR = Change in TR / Change in Q

where TR is total revenue from Q units, Marginal revenue is the marginal revenue from Qth unit and Q = quantity.

We can see from above that when Q = 30 then MR = Change in TR / Change in Q = (420 - 320)/(30 - 20) = 10

Hence MR = MC when Q = quantity = 30 units.

We can see from above table that When Q = 30 then consumers are willing to pay $14 and hence they will charge $14.

Assuming each firm will have equal market share thus quantity produced by each firm = Total quantity/ number of firms = 30/6 = 5.

Hence each firm will produce quantity = 5 units and will charge Price = $14