Question

Consider a price-taking firm that has total fixed cost of $500 and faces a market-determined price of $10 per unit for its output. The wage rate is $175 per unit of labor, the only variable input. Using the following table, fill in the columns and answer the question below.

(1)	(2)	(3)	(4)	(5)	(6)
Units of labor	Output	Marginal product	Marginal revenue product	Marginal cost	Profit
1	10
2	30
3	60
4	100
5	150
6	190
7	210
8	225
9	235
10	240

The manager should produce _____ units of output to maximize profit.

Answer 1

Marginal product is the change in the total output due to employment of additional unit of resource i.e. in this problem an additional unit of labor.

Revenue is the product of price and quantity sold i.e. Revenue = Price ×  Quantity sold

Marginal revenue product is the change in the total revenue due to employment of an additional unit of input i.e. in this case an additional unit of labor.

Total cost = Fixed cost + variable cost

Variable cost = Units of labor × wage rate per labor

Profit = Revenue - total cost

Units of labor	Output	Marginal product	Marginal revenue product	Marginal cost	Profit
1	10	_	_	_	-$575
2	30	20	$200	$175	-$550
3	60	30	$300	$175	-$425
4	100	40	$400	$175	-$200
5	150	50	$500	$175	$125
6	190	40	$400	$175	$350
7	210	20	$200	$175	$375
8	225	15	$150	$175	$350
9	235	10	$100	$175	$275
10	240	5	$50	$175	$150

The calculation related to the above table is shown as follows:-

Units of labor	Output	Marginal product	Revenue	Marginal revenue product	Total cost	Marginal cost	Profit
1	10		10 × $10 = $100	_	$675	_	$100 - $675 = - $ 575
2	30	30-10 = 20	30 × $10 = $300	$300 - $100 = $200	$850	850 - 675 = 175	$300 - $850 = - $ 550
3	60	60 - 30 = 30	60 × $10 = $600	$600 - $300 = $300	$1,025	1025 - 850 = 175	$600 - $1025 = -$425
4	100	100 - 60 = 40	100 × $10 = $1000	$1000 - $600 = $400	$1,200	1200 - 1025 = 175	$1000 - $1200 = -$200
5	150	150 - 100 = 50	150 × $10 = $1500	$1500 - $1000 = $500	$1,375	1375 - 1200 = 175	$1500 - $1375 = $125
6	190	190 - 150 = 40	190 × $10 = $1900	$1900 - $1500 = $400	$1,550	1550 - 1375 = 175	$1900 - $1550 = $350
7	210	210 - 190 = 20	210 × $10 = $2100	$2100 - $1900 = $200	$1,725	1725 - 1550 = 175	$2100 - $1725 = $375
8	225	225 - 210 = 15	225 × $10 = $2250	$2250 - $2100 = $150	$1,900	1900 - 1725 = 175	$2250 - $1900 = $350
9	235	235 - 225 = 10	235 × $10 = $2350	$2350 - $2250 = $ 100	$2,075	2075 - 1900 = 175	$2350 - $2075 = $275
10	240	240 - 235 = 5	240 × $10 = $2400	$2400 - $2350 = $50	$2,250	2250 - 2075 = 175	$2400 - $2250 = $150

The manager should produce 210 units of output to maximize the profit