4. Complete the steps in the derivation of the Fisher equation discussed on slide 17 of lecture 3 by showing that if we 1+i (a) Begin with = 1+r. 1+ 7 (b) Replace 1 with the Taylor-series expansion 1+ 7° 1 = 1- 7° + (7°)² - (7*)³ + (m*)ª – .. in the expression in part 4(a) above. (c) Assume that we can ignore any terms involving in“ or (7*)" for n > 2 because 7 is small. that we are left with the Fisher equation r = i – ".

Let A and B be two independent events such that P(A) = 0.25 and P(B) = 0.55- What is P(A or B)? Your answer should be given to 4 decimal places.

Consider the following Cobb-Douglas production function for the bus transportation system in a city:  Q = Lβ1Fβ2Bβ3 Where  L = labour input in worker hours              F = fuel input in gallons              B = capital input in number of buses              Q = output measured in millions of bus miles   Suppose that the parameters (α, β1, β2 and β3) of this model were estimated using annual data for the past 25 years. The following results were obtained: β1 = 0.45, β2 = 0.20 and β3 = 0.30 a.         Determine the (i) labour, (ii) fuel, and (iii) capital-input production elasticities

What conditions must non-linear time series models, such as vector autoregressive models, satisfy in order to use impulse response functions

4- The manager of Collins Import Autos believes the number of cars sold in a day(Q) depends on two factors: (1) the number of hours the dealership is open (H) and (2) the number of salespersons working that day (S ). After collecting data for two months (53 days), the manager estimates the following log-linear model: Q = aHbSc ----- a. Explain how to transform this log-linear model into a linear form that can be estimated using multiple regression analysis. b. How do you interpret coefficients b and c? If the dealership increases the number of salespersons by 20 percent, what will be the percentage increase in daily sales? c. Test the overall model for statistical significance at the 5 percent significance level.

Apply the properties of functions to correctly determine and interpret the break-even point in the following situations, using valid mathematical procedures and correct mathematical notation. Express your answer in terms of the context of the problem. The supply and demand equations for a certain product are: (1) and (2) respectively, where p represents the price per unit in dollars and q, the number of units sold per period. 3q - 200p + 1800 = 0 3q + 100p - 1800 = 0 Algebraically find the equilibrium price. Find and interpret the equilibrium price when a supplier tax of 27 cents per unit is imposed.