2. Consider Farmer Grover who grows corn Ｃ , which can be sold at a price of Ｐc per bushel. The number of bushels he grows is a function of the amount of time the farmer chooses to spend growing corn Ｎ , i.e. Ｃ＝Ｆ（Ｎ）. The marginal product of labor in corn production is positive but decreasing. The farmer also earns ter income of Ｙ. The farmer receives utility from consuming Ｚ , which he purchases at a price of Ｐz per unit and from leisure Ｌ . He has a time endowment of Ｔ hours and therefore Ｌ＝Ｔ－Ｎ . (A) If the farmer's utility function in Ｕ（Ｌ,Ｚ）, the what will be his utility maximization problem ？ (B) What are the first order and second order conditions in this problem ？ (C) Suppose the quantity of time the farmer chooses to spend growing corn is independent of Ｙ . Show that Ｎ will rise when Ｐc rises and present an intutive explanation of this result. --

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