1. Consider a rural peasant household growing a single crop such as maize or wheat. There are three inputs into the crop, labor (L), land (N), and water (W). Labor is available at wage w, land at a price v, and water is "free\" but fixed in a given supply available from a well on the household's land. Assume the production function is Cobb-Douglas and given by q = NaLW"\"', and the crop is sold at a market price P. There are two constraints, a working capital constraint equal to wL +vN S Q and a water constraint equal to W S W. a) Set up the household's profit function, substituting the water constraint Wfor W, and incorporating the working capital constraint with a Lagrangian multiplier (where we assume it binds). Take first order conditions with respect to labor, land, and your Lagrangian. b) In this context, what is your interpretation of the Lagrangian multiplier? c) Totally differentiate your first order conditions and obtain an expression for g and di. How dP = dW do changes in the crop price and in the access to a more plentiful water source influence the demand for working capital credit