b Complete the following table and answer the accompanying q

b) Complete the following table and answer the accompanying questions. notk a. At what level of the control variable are net benefits maximized? b. What is the relation between marginal benefit and marginal cost at this level of the variable? Marginal Net Benefit Control Variable Total Tetal Cost Net Benefits Marginal Benent MBO Marginal Cost MNBO Benefits BiO 1200 950O210 MCO 100 101 102 103 104 105 106 107 108 109 110 1400 1590 1770 1940 2100 60 70 80 90 100 110 120 2250 2390 2520 130 140 150 160 2640 2750

Solution

A) We are given the value of total benefit and control variable. We will find the values of marginal benefit by finding the difference between the total benefit of the concerned unit of control variable and total benefit at the preceding unit of control variable. For example, the marginal benefit of 101th unit of control variable is = total benefit of 101th control variable - total benefit of 100th control variable. This gives MB (at 101 units of control variable) = 1400 - 1200 = 200. Do the same for remaining portions.

Now find the total cost. We now use the reverse method and find total cost from marginal cost. Use the fact that

TC (at 101) = TC (100) + MC (101)

= 950 + 70 = 1020.

Similarly TC (at 108) = TC (107) + MC (108) = 1650 + 140 = 1790

This is true because marginal cost is the difference between the total cost of producing current units and the total cost of producting the preceding units.

The level of control variable at which Net benefits are maximum is 107. NB is 740

B) MB is closest to MC and positive at this level which should be true for maximizing net benefit.

Control variable	Total benefits	Total costs	Net benefuits	Marginal benefits	Marginal costs	Net margial benefit
100	1200	950	250	210	60	150
101	1400	1020	380	200	70	130
102	1590	1100	490	190	80	110
103	1770	1190	580	180	90	90
104	1940	1290	650	170	100	70
105	2100	1400	700	160	110	50
106	2250	1520	730	150	120	30
107	2390	1650	740	140	130	10
108	2520	1790	730	130	140	-10
109	2640	1940	700	120	150	-30
110	2750	2100	650	110	160	-50