Study Guide for Midterm: ECON 1003 1 Time, Structure, and Outline of the Test The midterm exam which counts for 35 percent of your grade will be held during class hours (9-11 am) on Thursday, October 7th, 2020. You will be able to access your exam on the Canvas Exam Portal. This is an open book take home exam. The sequence and structure of the exam is as follows. ˆ The exam will start at 9 am sharp. Make sure you are logged in to your Canvas Portal sufficiently before the start time. ˆ You will need to start the exam by clicking on Part A which consists of multiple choice/fill in the blank/True-False questions. There are 25 questions (each worth one mark) in part A and you will have 45 minutes to complete this part. At 9:45 am, your access to part A will close and your answers will be submitted. You cannot return to Part A after this. Note that you will have to enter an answer for a question before moving to the next question. You will also not be able to return to a question to change your answer. You will no longer be able to attempt questions in Part A after the 45 mins have elapsed. ˆ From 9:45 am you will have access to Part B of the exam which has two short answer questions. You will have 45 minutes to complete this part and the total marks for this part is 25. You will need to open the file for Part B, write your answers by hand, and make a pdf copy of your exam which you will upload on a designated space in the Canvas Exam portal. Only pdf files will be accepted and MAKE sure all your pages are together on one file. Multiple files will not be accepted. You will have a 30 minute grace period from 10:30 am to 11 am to upload your answers. From the point of view of the test, you should start with your lecture notes, tutorials and then the text book. You are responsible for the mate- rial from Lecture 1 to Lecture 6, and everything covered in the lectures and tutorials is examinable unless explicitly mentioned below. 1 When entering numerical answers for Part A, please bear the following in mind. ˆ In numerical questions where the answer is a whole number, you should enter that number. ˆ Where possible, you must enter a numerical answer. For example, if an answer is ln(2), you should write it in decimal form 0.69. ˆ Do not use regular fractions. For example, if an answer is 2/3, you can write it as 0.66 but not as 2/3. I have allowed for a range of answers so do not worry how you round the last decimal point. ˆ Do not add other symbols such as $ and %. If an answer is $150, write it as 150. If an answer is 15%, write it as 15. 2 What to Focus On 2.1 Lecture 1 1. Know the definition of a function. A function is a rule which assigns a unique real number to values of a variable in a domain. 2. Know the basic notation that we use for intervals. 3. Be able to work with simple applications of linear functions (for exam- ple, a linear demand function) and linear equations (for example, the budget line and the budget set). 4. Know how to find linear functions from the information given. For example, I can give you two points through which the line passes and ask you to find f(x). Or I can give you the slope and one of the points and ask you to find f(x). 5. Be able to solve for a simple system of linear equations. For example, you should be able to use a demand and a supply function to solve for the equilibrium price and quantity. 6. Work through the tutorial questions. 2 2.2 Lecture 2 1. In this lecture, we focus on non-linear functions and equations. 2. You should be able to work with quadratic, cubic, exponential, loga- rithmic, and hyperbolic functions. By work with I mean, you should be able to i) know the form of the functions, ii) plot the functions iii) solve equations and iv) understand the applications done in class. The text book has a lot of practice questions for solving equations. 3. Know that the exponential and logarithmic functions are inverses of one another. This is very helpful when solving equations. 4. Be able to work through simple economic applications like break even profits for a monopolist, supply and demand, and indifference curves. 5. Understand the concept of elasticity of demand which is the percentage change in quantity divided by the percentage change in price. Using derivatives, this can be written as ϵ = −dQ.P dP.Q . Note that I am consid- ering an absolute value here so that elasticity as defined, is a positive number. We will STICK to this definition in class. Some books includ- ing the text book define it as a negative number. 6. Work through the tutorial questions. 2.3 Lecture 3 1. Know that a derivative is a linear approximation of a function at a point. Geometrically, it is the slope of the tangent to the function. 2. Know all the rules for finding derivatives that we did in class. 3. Know what it means for a function to be increasing or decreasing and how this relates to the sign of the derivative. 4. Know how to find higher order derivatives and interpret them. 5. Know the definition of concave and convex functions (see lecture notes) and understand how they relate to the curvature of the graph of the function. 3 6. Be familiar with simple examples on risk aversion that we did in class. Loosely, an individual will need to compare two options where the individual’s expected wealth is the same but where one of the options involves uncertainty. The individual making the decision is assumed to have a utility function u(w) that is increasing in wealth. She computes her expected utility for each case and then chooses the option with a higher expected utility. Know that with a (strictly) concave utility function (with u′′(w) < 0) she will prefer the safe option (risk averse), with a (strictly) convex utility function (with u′′(w) > 0) she prefers the risky option (risk lover), and that for a linear utility function (with u′′(w) = 0), she is indifferent between both options (risk neutral). 7. Know how to plot functions using derivatives. Loosely, follow these steps. Find the points where the derivative of the function is zero. If there are finitely many of these, plot them on the horizontal axis, smallest to the largest. Then break the domain up into regions based on these points and for each region check if the derivative is positive or negative. If it is positive, the function slopes upward in this region and if it is negative it slopes downwards. Just as a side point, for this method to work, it requires the first derivative to be a continuous function. 8. Work through the tutorial questions. 2.4 Lecture 4 1. Know how to define an optimization problem. For example, a maxi- mization problem can be written as Max x f(x) subject to x ∈ S (that is subject to x lying in the set S). x is the choice variable which is chosen from the constraint set S and f is the objective function. 2. Know what local and global maximizers and minimizers are. x∗ is a global maximizer (or global maximum) if f(x∗) ≥ f(x) for all x ∈ S. x∗ is a local maximizer (or a local maximum)if f(x∗) ≥ f(x) for all x in a some small interval around x∗. The inequalities are flipped for a minimization problem. 3. Know the sufficient conditions for the existence of a solution to an optimization problem. For the case where the constraint set is an in- 4 terval the conditions are as follows. When the constraint set does not extend indefinitely (that is, when it is bounded), when it includes its end points (that is, when it is closed) and when the objective function is continuous on the constraint set, then a solution exists. Be able to construct examples of what can go wrong when you relax some of these assumptions. Know that these are sufficient conditions – they are not necessary for a solution to exist. 4. Know that a necessary condition for an interior point to be a (local or global) maximum is f ′(x) = 0. When the second derivative is negative at x this condition is also sufficient for a local maximum. When f ′′(x) ≤ 0 for all x in the constraint set then f ′(x) = 0 is both necessary and sufficient for a global maximum. 5. When the constraint set is an interval which includes its end points, the procedure for finding a global maximizer is as follows. Find all the stationary points with f ′(x) = 0. Compute the value of the func- tion at these points, and at the end points and compare these values. The point(s) which yields the largest value amongst these is the global maximizer. 6. Be able to work through the examples of monopoly and perfect com- petition that we did in class. 7. Work through the tutorial questions. 2.5 Lecture 5 1. Know that an indefinite integral can be thought of as an anti-derivative. 2. Know the rules for computing indefinite integrals that we did in class. 3. Know that a definite integral can be interpreted as the area between the graph of the curve and the horizontal axis. When the graph lies above the horizontal axis, this area is positive and when the graph lies below the horizontal axis, the area is negative. 4. Know how to compute definite integrals. In some cases, one of the bounds of the integral gets arbitrarily large (say b tends to infinity). If so, see what the antiderivative F converges to as b gets very large and use that value for F (b). 5 5. Be able to work through economic applications such as finding con- sumer surplus. 6. Know how to find the general and particular solutions for first order differential equations that we did in class. The text book has many practice questions on this. 7. Work through the tutorial questions. 2.6 Lecture 6 1. Know the definition of arithmetic and geometric sequences and series. 2. Know how to find the nth term of the sequence and know how to com- pute the sum of terms in the sequence. 3. Be able to work through compound interest problems, when interest rates are compounded annually and continuously. 4. Know the material on net present value, internal rates of return, and on annuities that we covered in class. 5. Work through the tutorial questions. 6