Question

Production/Cost Exercises
1. The following is a short-run production table for a firm with labor as its only variable input.
Wage = $ 200
Capital = 100 units
Capital Price= $40
Product Price= $120

Labor	Output
0	0
1	50
2	110
3	160
4	200
5	230
6	250
7	260
8	265
9	260
10	250

a. Determine the following measures at all levels of output:
MPL, APL, TFC, TVC, TC, TR, AVC, ATC, AFC, MC, PROFIT
b. At what level of output is the profit maximized?
c. What kind of observations can you make about MC, price, average total cost, and profit?

Answer 1

a)

In this example, the total fixed cost is the cost of capital = 100 units x $ 40 ( $ 4000)

Hence Total fixed cost = $ 4000

To calculate the variable cost, we multiply the cost of labor with the number of labors employed at each level of output.

MPL = Marginal product of labor.

MPL is the additional output produced for an unit increase in the labor input.

Average product labor is obtained by dividing the total product produced by the number of labors employed.

Total revenue (TR) = Product price x output

Average variable cost = ( Total variable cost ) Output

Total cost = Total fixed cost (TFC) + Total variable cost (TVC)

Average total cost (ATC) = (Total cost) Output

Average fixed cost = ( Fixed cost) Output

Marginal cost (MC) is the additional total cost incurred for an unit increase in the output.

Profit = Total revenue - total cost

The table below summarizes the measures

Labor	Output	Marginal product labor(MPL)	Average product labor(APL)	Total fixed cost(TFC)	Total variable cost(TVC)	Total cost	Total revenue(TR)	Average variable cost(AVC)	Average total cost(ATC)	Average fixed cost(AFC)	Marginal cost(MC)	Profit
0	0	_	_	$4,000	$0.00	$4,000.00	$0.00	_	_	_	-	-$4,000.00
1	50	50	50	$4,000	$200.00	$4,200.00	$6,000.00	$4.00	$84.00	$80	$200.00	$1,800.00
2	110	60	55	$4,000	$400.00	$4,400.00	$13,200.00	$3.64	$40.00	$36	$200.00	$8,800.00
3	160	50	53.34	$4,000	$600.00	$4,600.00	$19,200.00	$3.75	$28.75	$25	$200.00	$14,600.00
4	200	40	50	$4,000	$800.00	$4,800.00	$24,000.00	$4.00	$24.00	$20	$200.00	$19,200.00
5	230	30	46	$4,000	$1,000.00	$5,000.00	$27,600.00	$4.35	$21.74	$17	$200.00	$22,600.00
6	250	20	41.67	$4,000	$1,200.00	$5,200.00	$30,000.00	$4.80	$20.80	$16	$200.00	$24,800.00
7	260	10	37.15	$4,000	$1,400.00	$5,400.00	$31,200.00	$5.38	$20.77	$15	$200.00	$25,800.00
8	265	5	33.13	$4,000	$1,600.00	$5,600.00	$31,800.00	$6.04	$21.13	$15	$200.00	$26,200.00
9	260	-5	28.89	$4,000	$1,800.00	$5,800.00	$31,200.00	$6.92	$22.31	$15	$200.00	$25,400.00
10	250	-10	25	$4,000	$2,000.00	$6,000.00	$30,000.00	$8.00	$24.00	$16	$200.00	$24,000.00

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b)

From the table we can observe that at 265 units of output, the profit is $26,200.00 which is the maximum profit compared to all other levels of output. Hence the profit is maximized at 265 units of output.

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c)

From the table we can observe that the marginal cost remains constant for all levels of output. The product price remains fixed at $ 120. The average total cost starts decreasing as output increases and after reaching lowest level at an output of 260 , the average total cost starts increasing again.

The profit starts increasing as output increases and after reaching the maximum profit level of $ 26,200 at an output of 265 units, its starts to decrease again.