ECON300 Final Exam Study GuideProfessor CramtonUniversity of MarylandConcepts:- 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- x2convex, -x2concave - 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+no ln(ab) = lna +lnbo ln(ab) = blna * ln[e(x)]- Difference quotient: Δf/Δx = (f(x)-f(x0))/(x-x0)- Derivative: (f(x+Δx)-f(x))/Δx- Average Growth rate: v0erto Value at time 0: v0o Value at time T: vTo Decreasing slope = decreasing marginal utilityo Average rate change = secant, derivative = tangent- Linear: b, Quadratic: a(2x+Δx)+ b, Cubic: g(3x2+3xΔx+Δx2)+a(2x+Δx)+b- Growth of moneyo k compounds/year: xt+1 = xt(1+r/k)ko continuous compound: xt+1 = xtern- Perpetuity: d∞= 1/(1-∞)- Annuity: dn= (1-δn)/(1- )δ- Cobb-Douglas Function: y = x1αx2βo Links output per worker (Q) to capital per worker (K)o Q = Kα- Circular Flowo all endogenouso all solved simultaneouslyo both factor and product together- Average rate of change as Δx 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 – ΔQ - 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 Functionso Constant percentage growth per unit of time- Logarithmic Functionso Inverse of exponential functions- Most Frequent Compoundingo Once per year: (1+r)o Twice per year: (1+r/2)2o k times per year: (1+r/k)k = (1+1/m)mro ∞ times per year: (lim m∞(1+1/m)m)r=er- Real numbers all integers and numbers between the integerso Ex. ratios, fractions (rational numbers)- Integers a whole number- Interval set of all real numbers between 2 endpoints- Sets collection of itemso Elements in a set- Univariate functions maps one number, member of a domain, to one and only one number, element of the rangeo Ex. y = f(x) or y is a function of x- Domain set x- Range set of values that occur- Independent variable: x, dependent variable: y- 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
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