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In-Semester Exam, S2 2021 , ECON6001/ECON6701 Microeconomics Analysis I Instructions

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In-Semester Exam, S2 2021 , ECON6001/ECON6701 Microeconomics Analysis I Instructions. 1. You must submit all your answers as ONE HANDWRITTEN PDF FILE. The ?le upload link in on Canvas Exam site. In addition, there are a couple of numerical answers to parts of Question 2 and Question 3, which are displayed in blue below. Enter Quiz Portal, also reachable from the Canvas Exam site and enter your answers there. 2. Your score in this exam is worth 30% of your ?nal grade. Question 1 is worth 10 points, Question 2 and Question 3 are each worth 20 points. (Total 50 points). ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Question 1. There are two statements. You are required to comment on each of those statements. Answer in few sentences. You may even present your argument as a list of bullet points or make your point with a simple picture/example/counter example. Anything written over half an A4 page will be ignored. 1) First Welfare Theorem says that the competitive equilibrium allocation is Pareto E?cient under a very minimal set of assumptions. In view of this, provide at least two arguments for why there may (or may not) be a role for government. (5 pts) 2) We know that n di?erentiable functions x1(p; m); :::; xn(p; m) of prices and income are generated by some utility maximizing consumer if and only if each of them is homogeneous of degree P zero in prices and income, i.e. i pi xi(p; m) = m, and whose matrix of substitution terms (the Slutsky matrix) is negative semi-de?nite. This makes Afriat's Theorem and GARP unnecessary. Comment. (5 pts) -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Question 2. In an economy with Agent 1 and Agent 2, and two-goods (denoted by X and Y ) their indirect utility functions over prices p = (px; py ) and income m are v1(px; py ; m) = log (m) ¡ a log (px) ¡ (1 ¡ a) log (py) v2(px; py ; m) = log (m) ¡ (1 ¡ a) log (px) ¡ a log (py) (Noting @log(x) @x 1 = x will be helpful.) 1. Show that the Marshallian Demand functions of the two agents for good Y are given by y1(p; m) = (1 ¡ a) m py y2(p; m) = a m : py (10pts) 1 2. Now suppose the income is in fact dependent the value of the agents' endowments. The endowments of the two goods for the two agents are w1 = (2; 1) and w2=(1,3) respectively. Calculate the market clearing price ratio px / py as a formula. Next, enter its numerical value in Canvas Quiz portal for the particular value of a that is shown there. (No marks if you write just the numerical value correct without the working to show for it.) (5 pts) 3. Would you be able to calculate px and py if you used the market clearing condition for Good X as well? Justify your answer Just a para or two. (5 pts) -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Question 3 A certain household comprises of a couple, Adam (A) and Betty (B). They have lexicographic preferences over two goods G1 and G2 A wants to consume as much of G1 as possible, before moving on to G2 whereas, for B, it is the opposite, she wants to consume as much of G2 as possible before moving on to G1.1 Given their varying preferences, they decide to shop separately, after dividing the household income equally. The household income is $8. One di?erence to the usual setting there are government restrictions in place so that no individual is allowed to buy more than two units of either good. Hint: Do not use mathematical brute force (like Calculus) to solve this problem. A simple diagram with appropriate budget lines, etc. should su?ce. 1) Suppose prices are p = (p1; p2) = (1; 2). Denote the optimal choice of A and B as a = (a1; a2) and b = (b1; b2) respectively. Solve and calculate this explicitly. Enter the answer for a and b on the Canvas Quiz Portal. (No marks if you write just the numerical value correct without the working to show for it in the pdf upload.) (5pts) 2) Now suppose the prices change to q = (q1; q2) = (2; 1). Again, obtain the optimal choices for A and B, denote them by c = (c1; c2) and d = (d1; d2). Enter the answer for c and d on the Canvas Quiz Portal. (No marks if you write just the numerical value correct without the working to show for it in the pdf upload.) (5pts) 3) Now, you are an outside observer. All that you observe is that at p the household chose the bundle x = a + b was chosen and price q the bundle y = c + d was chosen. If you had mistakenly assumed that the household was a one individual, would you conclude that this individual is behaving rationally, i.e. maximizing a preference relation? Comment. (No essays just a few sentences, i.e. a paragraph or so, I will not read anything over 1/3 of a page.) (10pts) 1. Formally, for any pair of bundles x = (x1; x2) and y = (y1; y2), x a y , x1 > y1 or (x1 = y1 and x2 > y2) x b y , y a x: 2