幾題個體題目 - 經濟

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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