課程名稱︰個體經濟學一 課程性質︰經濟系必修 課程教師︰古慧雯 開課學院：社科院 開課系所︰經濟學系 考試日期（年月日）︰2015.01.12 考試時限（分鐘）： 120 mins 是否需發放獎勵金：是 試題 : 個體經濟學期末考(2015.1) 總分32分。答題皆須附說明，未做解釋的答案概不計分。 1. A has 12 units of x and 4 units of y. B has 8 units of x and 6 units of y. They have the same utility function： u = xy. (a) (2 points) Please derive the contract curve in an Edgeworth Box. (b) (3 points) A and B are both price takers. Let p denote the relative price of x. For instance, if p = 2, one could sell 1 unit of x in exchange for 2 units of y. Please derive the equilibrium relative price and solve for A's consumption bundle at the equilibrium. (c) (2 points) Please derive A's envy-neutral curve. (d) (1 point) Please find the region that both of them feel envy free. (e) (2 points) Please find the optimal allocation according to the maximin criterion (i.e. John Roawl's criterion) 2. (4 points) Consider Spence's model. There are 2 types of job applicants whose contribution to a firm and costs to obtain a diploma are as follows： ▕ A B ——————————————————————————— contribution to a firm ▕ $200 $160 cost to obtain a diploma ▕ $30 $50 Each type has the same number of people. Please find one pooling equilibrium and one separating equilibrium. (Specify employer's offers, and for each type of job applicants, specify their decisions about whether to obtain a diploma.) 3. In the last quarter of the nineteenth century, to encourage production and export of beet sugar, the German government gave a subsidy to beet sugar producers, s , for every unit of beet sugar exported. Britain produced refined cane sugar relying on colonial raw sugar supplies. The sugar price in Britain, p﹡, was set by the imported beet sugar price from Germany which was cheap and in a large quantity. British refined sugar producers protested against this "unfair competition" from abroad, and at the turn of the 20th century, the British govenment decided to tax imports of beet sugar to the degree how the German government subsidized her sugar producers. As a result,the sugar price in Britain increased from p﹡to p﹡+ s. Suppose in Britain, the domestic demand is negatively sloped and the domestic supply is positively sloped. Please draw a graph and show how this anti-dumping tax affected the British welfare for the folloing items： (a) (1 point) The change of consumer's surplus. (b) (1 point) The change of producer's surplus. (c) (1 point) The change of import tax revenue. (d) (3 points) Does this policy result in a net welfare gain or a deadweight loss to Britain? Please show your answer in the graph and explain intuitively why there is such a net result. 4. Product X is provided by a competitive constant-cost industry in which the production funtion of a manufacturer is as follows： q = (lk)^(1/4), where q denotes the output, l denotes units of labor and k denotes units of capital. The price to hire a unit of labor is $1, and the price to hire a unit of capital is $9. Besides that, a manufacturer needs to pay an annual license fee of $600. (a) (1 point) Please calculate the marginal rate of technical substitution of labor for capital, MTRS ≡ |dk/dl|. (b) (3 points) What is the long-run equilibrium price of X? (c) (2 points) In the short run, a manufacturer pays the license fee and fixes his k to be 81 units while l can be freely adjusted. What is his short-run supply function? 5. (4 points) In the second-hand market, depending on the quality of a car (H, M, L), a seller and a buyer value a car differently as follows： ▕ ▕ H M L ——————————————————— seller ▕ 100 75 50 buyer ▕ 120 90 60 The number of cars to sell for each quality type is 100; and on the other hand, buyers wish to purchase 300 cars in total. Suppose a car's quality is private information to its seller, and buyers make a rational guess of a car's quality. What is the equilibrium price? (Note： The equilibrium may not be unique.) 6. What is the elasticity of substitution of capital for labour? (a) (1 point) Suppose the production function is： f(K,L) = √(KL) , Please calculate its elasticity of substitution of capital for labor. (b) (1 point) According to Thomas Piketty, what is the range of the elasticity of substitution of capital for labor in the twenty-first century? --

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