Question

The Green Revolution (see the Mini-Case "Malthus and the Green Revolution") was based in part on extensive experimentation. The following data illustrates the relationship between nitrogen fertilizer (in pounds of nitrogen) and the output of a particular type of wheat (in bushels). Each observation is based on one acre of land and all other relevant inputs to production (such as water, labor, and capital) are held constant. The fertilizer levels are 20, 40, 60, 80, 100, 120, 140, and 160, and the associated output levels are 47, 86, 107, 131, 136, 148, 149, and 142 a. Use Excel to estimate the short-run production function showing the relationship between fertilizer input and output. (Hint: Select the data, insert a Chart, right click on Chart and on the '+ sign, use the Trendline option to regress output on fertilizer input. Try a linear function and try a quadratic function (polynomial setting with order 2), and determine which function fits the data better.) b. Does fertilizer exhibit the law of diminishing marginal returns? Fertilizer: f Output: o 20 40 60 80 100 120 140 160 47 86 107 131 136 148 149 142

Answer 1

linear trendline

160 140 10 TiHi 80 60 40 20 0 20 40 60 80 100 120 140 160 180

quadratic trendline

160 140 10 TiHi 80 60 40 20 0 20 40 60 80 100 120 140 160 180

q is plotted in the y axis and f at x axis, first the scatter chart is inserted and then trendline is added with linear specification and then polynomial of order 2. Quadratic fits the data better

Marginal return = change in quantity/ change in fertilizer, for eg. (86-47)/ (40-20) = 1.95
It explains the law of diminishing marginal returns as MR decreases as fertilizer applied increases

f	q	marginal return
20	47
40	86	1.95
60	107	1.05
80	131	1.2
100	136	0.25
120	148	0.6
140	149	0.05
160	142	-0.35