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[Exam Tutorial] ECO206 Term Test 1 Test Breakdown and Analysis

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ECO206 – Microeconomic Theory 1. Midterm I Structure Based on analysis of past midterms, there are five main topics that are covered in the first midterm of ECO206: Budget constraints, utility maximization, income and substitution effects, government grants/taxes and labor supply. The midterm is usually about 2 hours long and consists of 3 to 5 questions with 3 to 5 sub-questions per question. The total number of questions, including sub- questions, is roughly 12 to 15. 2. Midterm I Statistics Topics/Years 2009 2011* 2012 Budget Constraints 1 1 1 Utility Maximization 2 4 7 Income and 1 1 1 Substitution Effects Government 4 5 2 Grants/Taxes Labor Supply 4 3 4 Total 12 14 15 *In Midterm I of 2011, the test also included two questions on topics: normal goods and cross-price elasticity of demand. Neither of these topics appeared in midterm I of 2009, 2012. Midterm I Questions Statistics 8 7 6 Budget Constraints 5 Utility Maximization 4 Income and Substitution Effects 3 Government Grants/Taxes 2 Labor Supply 1 0 2009 2011 2012 Topic 1: Budget Constraints Knowledge Summary:  The budget constraint, for the purpose of the first midterm, gives a combination of 2 goods (x and y) that the individual can consume given his/her constraints: price of good x (p ), xrice of good y (p y and the individual’s income (E).  Critical assumption: the individual spends all his income on consuming goods x and y. Therefore we can write the budget constraint as: p xx + p *y = I  Furthermore, the budget constraint is a linear function and this tells us that the consumer is a price taker.  The three properties above help us derive the budget constraint graphically:  Slope: - (px)/(py), the slope is the measure of the opportunity cost  Moving from left to right along the budget constraint implies that we are consuming more of x and less of y.  A change in income (I) causes a shift in the budget constraint  A change in p cxuses the budget constraint to pivot through the vertical intercept (0, I/y ). An increase in x causes the budget constraint to pivot inward. A decrease in pxcauses the budget constraint to pivot outward.  A change in p cyuses the budget constraint to pivot through the horizontal intercept (I/px,0). Movement of the budget constraint is identical to the movement described in the previous bullet point. Summary of Questions to be asked:  Graphical representation of a budget constraint given 2 goods, their respective prices and the consumer’s income: graph the intercepts as shown in the graph above and connect them with a line, label the intercepts, the value of the slope and the axes.  Graphical change in the budget constraint due to changes in prices and/or income: recall – change in income  shift, and change in price  change in slope/pivot  Derive the budget constraint equation in order to solve an optimization problem: refer to utility maximization section below to see an optimization problem. Related Past Test Questions: 2012 Midterm 1 Question 1 2009 Midterm 1 Question 4a-i Topic 2: Utility Maximization Knowledge Summary: Key Components and Formulas:  Utility Function: mathematical representation of a preference order, assigning a number to each commodity bundle (x,y). Denote this function as U(x,y). The utility function helps us deduce which commodity bundles the consumer best prefers and least prefers.  Indifference Set: set of bundles that satisfies U(x)=Ȗ, for some arbitrary utility level Ȗ (i.e. Ȗ is a constant). These bundles are represented by an indifference curve shown below. All bundles on this indifference curve are equally preferred; therefore consumers are indifferent to any of them. Indifference curves to the right have higher utility and to the left have lower utility.  Marginal Rate of Substitution (MRS): is the slope of the indifference curve. It shows how much of good y a consumer is willing to give up, to consume more of x holding utility constant at Ȗ. The formula of the MRS is: =  How to derive the MRS: Totally differentiate the utility function U(x,y)=Ȗ Rearranging gives us: This represents the negative slope of the indifference curve. The MRS gives us the consumer’s willingness to substitute one good for another. With good y on the vertical axis and good x on the horizontal axis, the MRS represents the additional utility a consumer receives from consuming one more unit of good x (good on horizontal axis) and the loss of satisfaction from consuming less of good y (good on vertical axis).  Utility Maximization Problem: involves solving a constrained optimization problem combining a (i) utility function and a (ii) budget constraint. The utility function U(x,y) is the objective function and it is maximized subject to the budget constraint we derived earlier: p *x + p *y = I  px*x + p yy = I  To solve a maximization problem, it is essential to use the optimality condition:  Solving for x and y using this optimality condition and then substituting them into the budget constraint gives the optimal consumption bundle (x*, y*), example provided in past midterm questions below.  Graphically, it is the point of tangency between the indifference curve and the budget constraint.  2 Methods to solve: (i) substitution or (ii) Lagrangean Summary of Questions to be asked:  Derive the budget constraint, the marginal utilities of each good and the MRS  State the optimality condition  Solve a traditional constrained optimization problem involving maximizing a utility function subject to a budget constraint; may or may not specify method desired.  Graphically represent the point of tangency between the indifference curve and the budget constraint Related Past Test Questions: 2012 Midterm I Question 3 2009 Midterm I Question 1 Topic 3: Income and Substitution Effects Knowledge Summary:  The total effect of a price change can be decomposed into two effects: 1) the substitution effect and 2) the income effect  We use substitution and income effects in order to identify and classify different types of goods: normal goods, inferior goods, and Giffen goods.  Substitution effect is usually consistent for all types of goods, except Giffen goods: if the price of good x decreases and the price of good y remains constant, we will substitute more of good y for good x (i.e. if price of x decreases, quantity demanded of x increases and vice versa). Substitution effect induces an income effect because we have more income left over due to the decrease in price.  Income effects differ based on the type of good in question: - Normal good: if income increases, quantity demanded
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