Econ 300 Review Sheet for Final Examination As was the case for the first and second midterms, the upcoming exam will pose questions on: - terminology and notation - why economists use math - calculations typically applied by economists to solve economic problems We recommend that you prepare for the exam by completing two different types of tasks, described below as A and B. A. Work through the concepts listed below and make sure for each term you can recognize and apply: - the definition in words (in some cases what we have called “intuitive meaning”), - any corresponding mathematical expression, formula, or graph - the relevance to economic analysis As you do this, you should create a "cheat sheet" on a standard sheet of paper (two-sided). You can put whatever you like on this sheet of paper in whatever form you like, and can use it during the exam. Some of the concepts listed are mathematical terms which can be applied to economics, and some are economic terms that have a mathematical formulation; either way, you should understand the linkage between math and economics demonstrated by each concept. Some examples of these types of questions are provided to help you anticipate the way a concept leads to a question. More generally, you might find it useful to take each concept on the list and think of one or two possible exam questions similar to the examples but relevant to that particular concept. B. You should review all of the problem sets, the midterm exams, and the exercises presented in lecture and in discussion section, as many of the calculation-type problems on the exam are drawn from these exercises. You need to know when and how to apply each rule of differentiation. For example, you don’t want to apply the product rule to differentiate the function f(x) = 12 x + x2, but it would be useful for g(x) = (2x +1)(5x +7). List of Key Concepts and Terminology From first midterm: real numbers integers intervals sets univariate functions domain of a function range of a function validity of a function independent variablesdependent variables endogenous variables exogenous variables parameters intercept slope formula for a straight line formula for average rate of change secant line parabola increasing or decreasing functions strictly increasing or strictly decreasing functions monotonic functions inverse of a function multivariate functions Cobb-Douglas function isoquants and indifference curves extreme values: maxima and minima, global and local limits continuity concavity, strict concavity convexity, strict convexity exponential functions compound interest rates present value frequency of compounding continuous compounding logarithmic functions natural logarithmic functions growth rates systems of equations general equilibrium models partial equilibrium models differential calculus comparative statics difference quotient derivative instantaneous rate of change tangent line differentiability and the question of the existence of a derivative differential marginal cost marginal utility From second midterm: first derivative of a univariate function second derivative of a univariate function the relationships between second derivatives and concavity or convexity of a functionelasticity (point versus arc, income elasticity, own-price versus cross-price elasticity, etc., inelastic versus elastic versus unit elastic) average and marginal as applied to production or cost functions first-order partial derivative of a multivariate function with respect to a specific independent variable second-order partial derivative of a multivariate function with respect to a specific independent variable bivariate function diminishing marginal returns cross partial derivatives Young’s Theorem implicit functions isoquants the slope of isoquants marginal rate of substitution the multivariate differential homogeneous functions of degree k constant versus increasing versus decreasing returns to scale optimal outcomes (extreme values) stationary point first order conditions second order conditions sufficient conditions for a local minimum sufficient conditions for a local maximum After second midterm: constrained optimization substitution method Lagrange method Lagrangian Envelope theorem Shadow price Kuhn-Tucker method complementary slackness conditions probability addition rule mutually exclusive law of large numbers lottery expected value random variable probability distribution independence conditional probability expected utility risk averse, risk neutral, risk lover Pratt measure of risk aversion game theory normal form game best response mapping dominant strategy, dominated strategy, dominant strategy equilibriumnever a best response strategy iterated elimination of never a best response strategies Nash equilibrium mixed strategy equilibrium Example questions About notation: Given the function 12( , )y f x x we can use which of the following to denote the cross partial derivative with respect to x1 ? A. 12f B. ''f C. yx D. All of the above E. None of the above About the economic meaning of a mathematical concept: Suppose that a firm wants to choose the level of output which leads to the highest amount of profits. We could model this firm’s decision by expressing profits as a function of output and then: A. figuring out if that function is homogenous of degree 1 B. figuring out the value of output which leads to a local minimum C. figuring out the value of output which leads to a local maximum D. figuring out the cross partial derivatives E. figuring out the stationary point for the function About computation: Given the function 21 2 1 2 1 2( , ) 4 2f x x x x x x   , the second-order partial derivative with respect to 1x is: A. -2 B. 0 C. 2 D. 4 E. None of the