The per acre production function for rice is y = f (W, F ) = 2W^1/2 F^1/2 , where W is irrigation water, F is fertilizer and y is yield (output per acre).
1) Compute an expression for the marginal product of water.
2) Compute an expression for the marginal product of fertilizer.
3) Compute an expression for the marginal rate of technical substitution between fertilizer and water.
4) Derive the equation of the isoquant corresponding to the yield y = 4 in a graph with water on the horizontal axis. What is the shape of the isoquant? Draw the isoquant to scale on a graph with W on the horizontal axis.
5) What is the marginal rate of technical substitution when W = 2 and F = 2? Represent it on your graph.
6) Does the rice production function exhibit diminishing marginal rate of technical substitution? decreasing returns to scale?