Suppose there are two technologies that can be used for irrigation. Flood irrigation is relatively inefficient. For every 10 acre-feet of water applied to a n acre of land, only 3 are used by the plants. Drip irrigation is much more efficient; if 4 acre-feet of water is applied to the land, plants will actually consume 3 acre-feet. The production function is given by
y = 4e-0.25e2
where e denotes the amount of water actually consumed by the plants and y the output per acre. All land has identical quality. The price of water is $1 per acre-foot and the price of output is $2 per unit of output. Drip irrigation has a capital cost of $3 per acre, while flood irrigation has a capital cost of $1 per acre.
a) Derive the optimal applied water use for each of the two technologies.
b) Identify which technology will be chosen. Explain your answer.
c) Discuss how your answer would change if the effectiveness of drip and flood irrigation depended on land quality. Your answer should indicate both the likely outcome and the reason it occurs.