Question

Tom, the only steel drum manufacturer in Narnia, can sell a single drum for $30. However, for every extra drum he wants to sell, he is forced to reduce the price (for all his customers) by $2. The total fixed costs in his workshop are $15, and the variable cost of the first drum produced is $25. For each extra drum thereafter, the cost drops by $5 up to, and including, the fifth drum. After that, the cost of each extra drum increases by $5.

What is Tom’s profit-maximizing output, price, and total profit or loss?

Output:

Price: $   

Profit/loss: $

Answer 1

Given,

When Q = 1, Price = $30

Price decreases by $2 for every 1 unit increase in Q.

Fixed cost = $15

Variable cost of the first unit = $25

Variable cost decreases by $5 for each extra drum up to 5 units and then increases by $5 for each extra drum

From the above data, the following table can be constructed

Quantity (Number of steel drums)	Price ($)	Total Revenue ($)	Marginal Revenue ($)	Fixed Cost ($)	Variable Cost ($)	Total Cost ($)	Marginal Cost ($)	Profit ($)
0	32	0	-	15	0	15	-	-15
1	30	30	30	15	25	40	25	-10
2	28	56	26	15	45	60	20	-4
3	26	78	22	15	60	75	15	3
4	24	96	18	15	70	85	10	11
5	22	110	14	15	75	90	5	20
6	20	120	10	15	85	100	10	20
7	18	126	6	15	100	115	15	11
8	16	128	2	15	120	135	20	-7
9	14	126	-2	15	145	160	25	-34
10	12	120	-6	15	175	190	30	-70

Formulae used:

Marginal Revenue from Nth unit = Total Revenue from N units - Total revenue from (N-1) units

Marginal Cost of Nth unit = Total Cost of N units - Total Cost of (N-1) units

Profit = Total revenue - Total cost

Profit-maximizing rule:

Profit is maximized at the maximum quantity up to which the marginal cost remains less than or equal to the marginal revenue.

From the table, we observe that Marginal Cost = Marginal Revenue = $10 at a quantity = 6 units

Therefore, the profit-maximizing output = 6 units

When Q = 6 units, Price = $20 (obtained from the table)

Profit = Total Revenue - Total Cost = $120 - $100 = $20