ECON300 Final Exam Study Guide Professor Cramton University of Maryland Concepts No compounding x1 x0 1 r n where x1 future value and x0 present value Discrete compounding x1 x0 1 r k kn Continuous compounding x1 x0 ern x2 convex x2 concave isoquant same y output level in Q Monotonic doesn t have to be strictly anything Continuous compound formula Pert Present value compounded xt xt n 1 r n Annual interest rate 1 r nxt n o ln ab lna lnb o ln ab blna ln e x Difference quotient f x f x f x0 x x0 Derivative f x x f x x Average Growth rate v0ert o Value at time 0 v0 o Value at time T vT o Decreasing slope decreasing marginal utility o Average rate change secant derivative tangent Growth of money o k compounds year xt 1 xt 1 r k k o continuous compound xt 1 xtern Perpetuity d 1 1 Annuity dn 1 n 1 Linear b Quadratic a 2x x b Cubic g 3x2 3x x x2 a 2x x b Cobb Douglas Function y x1 x2 o Links output per worker Q to capital per worker K o Q K Circular Flow o all endogenous o all solved simultaneously o both factor and product together Average rate of change as x approaches 0 Mating Game N e maximizes probability of best selection The function y 1 x is concave convex and linear TR P Q where P 5 Q average rate of change total revenue 5 2Q Q Y 20 8x x3 differential is 3x2 8 dx Monopolist selects output to maximize profits then output will be on the elastic portion of the demand curve Exogenous determined outside the model Endogenous explained by model Exponential Functions o Constant percentage growth per unit of time Logarithmic Functions o Inverse of exponential functions Most Frequent Compounding o Once per year 1 r o Twice per year 1 r 2 2 o k times per year 1 r k k 1 1 m mr o times per year lim m 1 1 m m r er Real numbers all integers and numbers between the integers o Ex ratios fractions rational numbers Integers a whole number Interval set of all real numbers between 2 endpoints Sets collection of items o Elements in a set Univariate functions maps one number member of a domain to one and only one number element of the range o Ex y f x or y is a function of x Independent variable x dependent variable y Domain set x Range set of values that occur Parameters a given constant Secant line rate of change in a function Slope the change in value of the function associated with a given change in its argument Average rate of change ratio of change of the value of dependent variable to the change in the value of the independent variable over interval
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