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 – ".
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- I cannot figure out how the equation goes from q1 = D1 (p1; p2) = S(1/2 + (p2-p1/2t)) to q1 = S/2 +(p2-p1/2t) why is S not in the numerator of both terms? i.e. q1 = S/2 + S(p2-p1/2t)Q6 Suppose that at time t=0, half of a "logistic" population of 100000 persons have heard a certain rumor and that the number of those who have heard it is then increasing at the rate of 500 persons per day. How long will it take for this rumor to spread to 80% of the population? ( Suggestion: Find the value of k by substituting P(0) and P'(0) in the logistic equation) a. About 98 days b. About 34 days c. About 19 days d. About 69 days e. About 119 days3. Suppose that individuals with a strong enthusiasm for technology are willing to pay $500 now for the latest iPhone, but only $350 if they must wait a year. Normal people are willing to pay $250, and their desire to purchase does not vary with time. Assume for simplicity that there are equal numbers of each customer type (strong enthusiasm and normal), that the MC of the iPhone is $100, ignore the time value of money, and there are only two years. (Hint: With discrete problems consider all the different options and evaluate each of them to determine the optimal strategy. In this case, there are only three prices given and two time periods, so a total of 6 pricing strategies exist but some of them will.) What is the highest profit level that can be achieved if the price for an iPhone is fixed for both years (uniform pricing)? What is the highest profit level that can be achieved if the price for an iPhone can be altered across the two years?
- COVID-19 brought global economic and financial ramifications that were felt through global supply chains, from raw materials to finished products. Some term it as a black swan event that may finally force many companies, and entire industries, to rethink and transform their global supply chain model. If you are the CEO of a U.S. based company which is heavily dependent on foreign locations for sourcing and manufacturing, how would you make short-term and long-term plans to modify your supply chain model? List and discuss the main considerations or factors that will influence your decision.Q4 A business manager determines that t months after production begins on a new product, the number of units produced will be P thousand,where P(t) =6?2 + 5? /(? + 1)2 production in the long run (i) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture.Turbulence makes it difficult to directly measure the thickness of the slick at the source (where x = 0),but for x > 0,it is found that y =0.5(x2 + 3x)/ x3 + x2 + 4x Required:a)Assuming the oil slick is continuously distributed,how thick would you expect it to be at the source?The Financial Markets proficiency has been more inclined to interest rates productssuch as loans and term deposits in Zambia than structured products. With the adverseeconomic repercussions that countries, including Zambia experienced during theoutbreak of COVID-19, the market has moved to structured products provision such asoptions, forwards, to mention but a few. The implementation of risk mitigation strategicby most companies made the financial market to enhance structured products that aresuitable to hedge all risks arising from investments and business operations.Assuming Zambeef employees you as the Investment Hedging Director to manage theinvestment in Zambia, you approach your bank, Standard Chartered Bank to structurean option to help hedge Zambeef future shares transactions. You enter into a 5 yearscall option contract at an exercise price of K350 and paid option premium amounting toK50. Three years later, the company has an increase in operational needs and decidesto assess…
- As a manager of a small software retailing company, you are concerned with projected profit next year. While profit can be determined as the difference between sales and maintenance cost, or in symbols, P = S - M, where P is profit, S is sales, and M is maintenance cost including technical support. It is argues that when sales goes up so does maintenance cost because the cost of technical support will go up. Further, it is measured that the correlation between S and M is 0.8. Now given the figure that sales next year is expected to be $300 thousand with standard deviation of $4 thousand and maintenance cost is expected to be $150 thousand with standard deviation of $6 thousand, what would be the expected profit and its standard deviation you will include in your report?Give typing answer with explanation and conclusion Suppose that the government must undertake an irreversible policy decision regarding the extent of air pollution regulation. The government is making this decision in a situation of uncertainty, however. In particular, there is some probability p that the benefits will remain the same as they are this year for all future years, but there is some probability 1 - p that benefits will be less in all future years. If we take into consideration the multiperiod aspects, should we err on the side of overregulation or underregulation, compared to what we would do in a single-period choice?Cobb-Douglas production function 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 estimate using annual data for the past 25 years. The following results were obtained: β1 = 0.45, β2 = 0.20 and β3 = 0.30 Suppose that capital input (number of buses) is decreased by 3 percent next year (which, certain older buses are taken out of service). Assuming that the other inputs are held constant, determine the approximate percentage change in output. What type of returns to scale appears to characterize the transportation system (ignore the issue of statistical significance)? Discuss some of the methodological and measurement problems one might encounter in using time-series data to estimate the parameters of this model.
- Is this right or wrong (The question is the screenshot) (A) We want to minimize the cost function C(x, y) = 9x + 12y subject to the constraint U(x, y) =x (y + 3) = 128.9 and non-negativity constraints × ≥ 0 and y ≥ 0 We set up the Lagrangian: L(x, y, λ) = C(x, y) - λ(U(x, y) - 128.9) Now, we calculate the partial derivatives with respect to x, y, and 1: ∂L/∂x = 9 - λ(y + 3) ∂L/∂y = 12 - λX ∂L/λ = 128.9 - U(x, y) Setting these partial derivatives equal to zero, we have: 9 - λ(y + 3) = 0 2 12 - λx = 0 128.9 - x(y + 3) = 0 From equation 2, we get λ= 12/x. Substituting A into equations 1 and 3: 9 - (12/x)(y + 3) = 0 2. 128.9 - xY - 3x = 0 Now, we can solve this system of equations simultaneously. Let's start by solving equation 2 for X: 128.9 - xy - 3x = 0 xy = 128.9 - 3x Now, substitute this into equation 1: 9 - (12/x)(y + 3) = 0 9-(12/x)(128.9 - 3x + 3) = 0 9- (12/x)(131.9 -3x) = 0 9 -1,582.8/x + 36x = 0 Multiply through by x to get rid of the fraction: 9x - 1.582.8 ÷…Q: Determine whether the following statemnts are true or false: a) If the firm increases the volume of used resources by 30%, and the volume of production thus increases by 20%, then there is a positive effect of the production scale. b) Average fixed costs decrease as production increases. c) The economic profit usually exceeds the accounting profit.Suppose that a house loan of $1,000,000 is to be paid off by equal monthly payments of $ d over the course of 30 years. Suppose that the loan accrues interest at a rate of 1%, compounded monthly. Let Yn be the amount of money owed at the beginning of the n-th month; thus, yo = 1,000,000 and the first payment and first interest charge both occur at time n = 1. (a) Show that the causal sequence yn satisfies yn = 1.014n-1 +1,000,0008,-dun-1. (b) Use the 2-transform to solve for yn (c) Set Y360 = 0 in order to solve for d. (d) What is the total sum of payments made over the 30 years?