Joe Grow, an avid indoor gardener, has found that the number of happy plants, h, depends on the amount of light, l, and water, w. In fact, Joe noticed that plants require twice as much light as water, and any more or less is wasted. Thus, Joe’s production function is h = min{l, 2w}.
(a) Suppose Joe is using 1 unit of light, what is the least amount of water he can use and still produce a happy plant?
(b) If Suppose Joe wants to produce 4 happy plants, what are the minimum amounts of light and water required?.
(c) Joe’s conditional factor demand function for light is l(w1, w2, h) = h and his conditional factor demand function for water is w(w1, w2, h) = ____.
(d) If each unit of light costs w1 and each unit of water costs w2, Joe’s cost function is c(w1, w2, h) = _____.