課程名稱： 進階個體經濟學 課程性質： 選修 課程範圍： Pindyck Ch6生產 & Ch16一般均衡與經濟效率 開課教師： 鄭鴻章 開課學院： 商學院 開課系級： 國貿系 考試日期(年月日)： 2012/4/13 (Fri) 考試時限(Mins)： 110 min 試題本文： 一、問答及計算(25%) 1) Leann's Telecommunication firm production function is given by y(K,L)=200(KL)^(2/3), where K is the number of internet servers and L is the number of labor hours she uses. Does this production function exhibit increasing, constant or decreasing returns to scale? Holding the number of internet servers constant at 8, is the marginal product of labor increasing, constant, or decreasing as more labor is used? 2) Homer's boat manufacturing plant production function is y(K,L)=(√K)^5*(√L) where K is the number of hydraulic lifts and L is the number of labor hours he employs. Does this production function exhibit increasing, decreasing or constant returns to scale? At the moment, Homer uses 20,000 labor hours and 50 hydraulic lifts. Suppose that Homer can use any amount of either input without affecting the market costs of the inputs. If Homer increased his use of labor hours and hydraulic lifts by 10%, how much would his production increase? Increasing the use of both inputs by 10% will result in Homer's costs increasing by exactly 10%. If Homer increases his use of all inputs by 10%, what will increase more, his production or his costs? Given that Homer can sell as many boats as he produces for $75,000, does his profits go up by 10% with a 10% increase in input use? 3) Apu's Squishy production function is y(K,L)=K*(√L) where K is the number of squishy machines and L is the number of labor hours he employs. Does this production function exhibit increasing, decreasing or constant returns to scale? At the moment, Apu uses 2 squishy machines and 4 labor hours. Suppose that Apu can use any amount of either input without affecting the market costs of the inputs. If Apu increased his use of labor hours and squishy machines by 100%, how much would his production increase? Increasing the use of both inputs by 100% will result in Apu's costs increasing by exactly 100%. If Apu increases his use of all inputs by 100%, what will increase more his production or his costs? Given that Apu can sell as many squishies as he produces for $1.00, do his profits go up or down when he increases his input use by 100%? 4) Marge's Hair Salon production function is y(K,L)=√(KL) where K is the number of hair dryers and L is the number of labor hours she employs. Does this production function exhibit increasing, decreasing, or constant returns to scale? At the moment, Marge uses 16 labor hours and 16 hair dryers. Suppose that Marge can use any amount of either input without affecting the market costs of the inputs. If Marge increased her use of labor hours and hair dryers by 10%, how much would her production increase? Increasing the use of both inputs by 10% will result in Marge's costs increasing by exactly 10%. If Marge increases her use of all inputs by 10%, what will increase more her production or her costs? Given that Marge earns $12.50 for each unit produced, do her profits go up or down when she increases her input use by 10%? 二、In the analysis of an exchange between two people, suppose both people have identical preferences. Will the contract curve be a straight line? Explain. Can you think of a counter example? (15%) 三、請利用下列模型：（符號意義如上課所示）(20%) ＿ ＿ Min C = PL(L是下標)*L+PK(K是下標)*K _ s.t Q = A*L^α*K^β 求出成本極小時之L與K值（即L、K之需求函數） 四、請分別利用一般均衡與部分均衡分析，探討兩國貿易時， 　a)貿易型態如何決定？　　╮ b)交易條件如何決定？　　├ (20%) c)貿易利得為何？　　　　╯ 五、請詳細推導生產可能曲線，並解釋其經濟意義。 (20%) --

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