Question

1. Suppose you are a farmer and there are two technologies that can be used for irrigation. Flood irrigation is relatively inefficient: for every 10 acre-feet of water applied to an acre of land, only 3 af are used by the plants. Drip irrigation is much more efficient: if 4 acre-feet of water are applied to the land using this technology, plants will actually consume 3 af. The agronomic production function is given by y = 4e − 0.25e2, where e denotes the amount of water actually consumed by the plants and y denotes 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.

   1. (a) Derive the optimal amounts of applied water using each of the two technologies.

   2. (b) Identify which of the two technologies will be chosen. Explain your answer.

   3. (c) In five sentences or less, explain how your answer might change if the effectiveness of the two irrigation technologies varied by land quality. Use economic reasoning to make a prediction about which direction your answers would change and justify why your prediction makes economic sense.

Answer 1

ANSWER:

GIVEN DATA

y = 4e − 0.25e2

where:

e denotes the amount of water actually consumed by the plants

and y denotes the output per acre