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AY 2018-2019
Simulation Mid Term test Microeconomics II Prof. Nicola Dimitri
You can use the calculator if needed. Smartphones, lecture notes and books are not allowed. You have 1 hour and 30 minutes.
1. (11 points)
Consider the following Cobb-Douglas technology with one output 𝑧 and two inputs, 𝑥 and 𝑦, 𝑧 = 𝑓(𝑥, 𝑦) = 𝑥𝑎𝑦1−𝑎
where 0 < 𝑎 < 1. If 𝑤𝑥 and 𝑤𝑦 are, respectively, the unit proces of 𝑥 and 𝑦 find the cost function associated to this technology.
2. (11 points)
Discuss the notion of Walrasian Equilibrium and the proof of its existence.
3. (11 points)
Consider the Arrow Debreu (AD) economy seen in class, with one commodity, two consumers 1 and 2, and two states 𝐴 and 𝐵. Suppose the endowments are 𝜔1= (1,0) for the first consumer and 𝜔2= (0,1) for the second consumer. Finally, assume that for both consumers the utility function is 𝑈(𝑐) = 𝑐𝑎 with 0 < 𝑎 < 1 and that they share the same probabilities over the two states. Find the AD (price and allocation) equilibrium of the economy.
Program 1st part
Production theory, Walrasian Equilibrium, Arrow-Debreu Equilibrium
Rules mid term test
Remind that the grade of the mid term can be kept until the two tests in September 2019, included. The second part can be taken at any test until September included. If you fail the second part, or reject the grade of the second part, you have to re-take the whole test.
