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2015-03-10
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Suppose there were only two types of footballs in Spain: Asado, produced byLionel Messi, and Port, produced by Cristiano Ronaldo. Both these footballs use rubber and leather in their production processes, which involve concave, increasing, differentiable and constant returns to scale production functions. However the leather to rubber ratio in production is always higher in Asado than in Port. Both these footballs are sold in the world markets. Both leather and rubber are immobile. Furthermore, all leather and rubber is owned by consumers,and can only be used as inputs for the production of footballs within Spain. We are consider-ing Spain as a single economy. Both Asado and Port are produced in strictly positive quantities.

a.Discuss whether the following statements are true or false. Note: you should use either a diagrammatic approach or a mathematical approach with your discussions.
Statement 1: “If the price of Asado increases, then more of Asado will be produced”
Statement 2: “Suppose all leather is owned by consumers living in Barcelona and all rubber is owned by consumers living in Madrid. Given that the price of Asado increases, we would expect those consumers living in Madrid to be happier”

b. Would your arguments for the statements above change, had the rubber to leather ratio in production been higher for Asado? Discuss.      
                        
               

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2015-4-2 15:29:57
这个题目要设定两个生产函数才行,
Q1 = \alpha log Leather + (1 - \alpha) log Rubber,
Q2 = \beta log Leather + (1 - \beta ) log Rubber
两种生产要素比的差异为:\alpha/(1-\alpha) > \beta/(1-\beta)。
假设生产要素价格不变,收入为
I1 = Leather,
I2 = Rubber.
再看题目。
a statement 1: 不证自明。想证明请设定效用函数就行了。
   statement 2: 由于A对Leather 的需求量超过 Rubber,所以I1大于I2。
b 会变化。
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