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- Title: Micro Theory Test 1 2006 for posting
- Type: Notes
- School: UCF
- Course: ECO 6938
- Term: Fall
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6118 ECO Advanced Micro Economic Theory Professor Elisabet Rutstr m MIDTERM TEST 1 October 3, 2006 Please work out your answers on a separate paper and then write your answer neatly in this test form. Make sure that you include all your derivation steps and prove your answers completely. Each question has equal weight. Question 1 Specify an objective function for a perfectly competitive firm that maximizes profits net of a concern for the fact that output generates pollution, i.e. objective function includes an effect from pollution that is negative. Assume that the propensity to pollute is in fixed proportion to output. The function that relates utility to this pollution needs to be general, however. a) Specify the pollution function: b) Specify the argument in the utility function that relates utility to this pollution function: c) Specify the objective function: d) Verify that the objective function fulfills the second order sufficient conditions for uncontrained maximization. What are the additional requirements compared to a firm that is only profit maximizing? Question 2 For the following production function f ( x) = x1 1 Derive the expression for a) the profit function b) Verify that the function fulfills the convexity property of the profit function with respect to the factor price. Question 3 Under conditions what can we form refutable hypotheses in unconstrained optimization problems? Derive the general comparative statics expression for one choice variable from a two variable optimization problem to show this. Do not specify this as a profit maximization problem. Question 4 Cox (2003) specifies an investment game with two players, and investor and a contractor. Both are given an initial endowment of $10, and the investor then has the option to send some of this money to the contractor. Any money that is sent triples due to the successful investment. It is then up to the contractor whether he wants to send some money to the investor or not. a) What are the three assertions that Cox discusses as candidates for explaining how people would behave in this game, and what is the predicted behavior for each? 1. 2. 3. b) What is the empirical problem that Cox is addressing in this paper with his proposed experimental design? Show clearly why this is a problem. Question 5 a) What property of a production function makes it possible for us to transform the entire isoquant mapping into the unit isoquant? b) Show how this is possible. c) What does this property imply for the Marginal Rate of Technical Substitution at different output levels found along a ray from the origin? Show in a graph. No other proof is necessary.
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