business question

You are the actuary to a large UK defined benefit pension scheme which provides a range of pensions and life assurance benefits. The employer currently contributes 20% of salaries to this scheme and members contribute at the rate of 5%. The Human Resource (HR) director has approached you and suggested that as employees do not appreciate the pensions package, the value of this is to be notified to them as part of the annual exercise which informs them of their salary increase. (i) Outline the points to be included in a letter to the HR director explaining why it would not be appropriate for the value notified to employees to be the rate of contribution currently being paid by the employer to the scheme. [8] (ii) It is decided to use an approach which expresses the cost as a percentage of the employee s salary, the relevant percentage is age-related. Discuss the issues to be considered in setting the assumptions to be used to determine the relevant table of percentage rates. [18] (iii) Describe two alternative approaches of establishing the value to be shown and list any particular problems that these could give rise to. [6] (iv) Five years later, you are asked to draft a letter responding to a member who has complained. Based on the information supplied on his annual statements, the member was expecting his pension benefits to have a current value of 70% of his salary, whereas the transfer value he has been offered as an alternative to his deferred benefits is approximately half of this amount. Outline the points to be included in the letter. [7] (v) Having read the reply, the member responds that he has approached a financial adviser who has told him that the transfer value offered is only sufficient to buy a deferred annuity of one-third of the scheme deferred pension. Outline the points to be included in the reply to this subsequent letter

Assume that the Phillips curve is given as: t = te + 0.1 - 2t a) What is the natural unemployment rate? Now the expectations for inflation are: te = (1 - ) + t-1 can be any constant value, either 0 or another number above zero. First assume that = 0 and that t = n (ie the unemployment rate is equal to the natural unemployment rate). In year the government authorities decide to reduce unemployment to 3% and keep it there forever. b) Determine inflation for the years + 1, + 2, + 3, + 4, + 5. c) Do you think the answer you gave to b) makes sense? d) Now suppose that the year + 6 increases from = 0 to = 1 and that the authorities are still determined to keep at 3% forever. e) Why does it make sense for to increase in this way? f) Determine inflation for the years + 6, + 7 and + 8. Also show your answer diagrammatically

6. (10) Consider a standard growth model in discrete time. Throughout this question you can focus on the Social Planners problem (vs the more complicated model with competitive markets). At t = 0 there is a large number of identical agents normalized to 1. The population grows at rate n per period, i.e., Nt = (1 + n) t . The representative agents preferences are described by U(fctg 1 t=0) = X1 t=0 t c 1 t 1 : The initial capital stock in this economy is K0, and each agent can devote one unit of productive time (in each period) to work. Final output is produced using capital and labor, and production is characterized by the so-called labor-augmenting technology: Yt = F(Kt ; Nt(1 + g) t ); where F is a CRS production function. Capital depreciates at rate 2 (0; 1). The Social Planner wishes to maximize per-capita life-time discounted utility. (a) Describe the resource constraint of the Planners problem. Hint: It will be useful express all the variables into growth-adjusted per-capita variables, as we did in class. (b) Characterize the optimal solution to the Planners problem (i.e. derive the Euler equation). (c) What happens to per-capita consumption in the long run? What happens to total consumption in the long run? (For full credit I expect you to derive the results carefully, and relate them to your work in part (b). However, partial credit will be given to correct, intuitive answers

2. Suppose a country has a money demand function: (M/P)d = kY, where k is a constant parameter Let's assume that the Money Supply grows by 10%/year and Real Income grows by 3%/year. a) What is the average rate of inflation? b) If real income growth was higher, how would that affect the inflation rate? Explain. c) What is the economic meaning of k? How is it related to monetary velocity? Explain. d) If the growth rate of monetary velocity increased steadily due to technical innovations, how would that affect the rate of inflation? Explain.

Suppose that a country experiences a reduction in productivity due to an increase in regulations on its energy sector. This is the equivalent of an adverse shock to the country's production function.

a) What will happen to the labor demand curve? Explain. b) How would this change in productivity affect the labor market - that is employment, unemployment, and real wages - once the labor market reaches a new equilibrium? c) How would this change in productivity affect the labor market in a country where the unionization of the labor force is relatively high and unions prevent real wages from falling?

Consider the Solow growth model in which population evolves according to: N = (1 + n)N where N is the population (labor force) in the current period, N is the population (labor force) in the future period, and n is the population growth rate. There are public health expenditures that takes the form of government spending, G = gN, where G is the current period government spending on health care, g is the per-capita health spending in the current period. The production technology is given by Y = zKN1 where Y is the output of the consumption good, z is the total factor productivity, K is the current period capital stock, aN is the labour input, and 0 < < 1 is a parameter. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1. (a) Suppose that the economic is hit by a pandemic (e.g. Covid-19). The government responds to the pandemic by raising the public health spending per person (e.g spending on vaccination) temporarily (i.e. one-period only). Using the Solow growth model, assess the impact of the pandemic. (b) Suppose that the economic is hit by a pandemic (e.g. Covid-19) which causes a temporary decrease in total factor productivity, z, as certain sectors in the economy (e.g. entertainment, travel etc.) cannot deliver the same quantity of output with physical distancing measures. In order to counteract the decrease in z due to the pandemic, the government increases temporarily G (i.e. spending on vaccines) which eliminates the pandemic in the future period completely. Using the Solow growth model (i.e. equations, graphs, and words), discuss the changes in economic variables in both periods.

QUESTION 1 It is common knowledge between Countries 1 and 2 that Country 1 plans to attack Country 2. The attack can occur at one of two locations, C and D. The success or failure of the attack depends on three factors: where Country 1's troops are amassed prior to the attack (near C or near D), where the attack occurs, and which location is defended. Let x denote the fraction of Country 1's troops amassed near C, and (1-x) the fraction of Country 1's troops amassed near D (0x1). The game is played as follows: simultaneously, Country 1 chooses to attack either C or D, and Country 2 decides to defend either C or D. There are only two possible outcomes, from the point of view of Country 1: Success and Failure. Country 1 strictly prefers Success to Failure and Country 2 has the opposite ranking. The two countries have von Neumann-Morgenstern preferences over lotteries involving these two outcomes. The probability of a successful attack is determined as follows. Let z denote the fraction of Country 1's troops amassed near the location where Country 1 attacks (so z = x if Country 1 attacks at C, and z= 1-x if Country 1 attacks at D). Then the probability of a successful attack is z if Country 2 does not defend the location where Country I attacks, andzif Country 2 does defend the location where Country I attacks. For parts (a)-(f) assume that the value of x is fixed and cannot be changed; furthermore, the value of x is common knowledge between the two countries. (a) Write a strategic-form game that represents the situation described above. (b) Is there a range of values of x for which Country 1 has a dominant strategy? If so, state the range and specify whether it is strict or weak dominance. fe) Is there a range of values of which Connte 26

If a firm adheres strictly to the residual dividend policy, a sale of new common stock by the company would suggest that a. The dividend payout ratio has remained constant. b. The dividend payout ratio is increasing. c. No dividends were paid for the year. d. The dividend payout ratio is decreasing. e. The dollar amount of investments has decreased. 131. If a firm adheres strictly to the residual dividend policy, then if its optimal capital budget requires the use of all earnings for that year (along with new debt according to the optimal debt/total assets ratio), the firm should pay a. No dividends except out of past retained earnings. b. No dividends to common stockholders. c. Dividends, in effect, out of a new issue of common stock. d. Dividends by borrowing the money (debt). e. Either statement c or statement d above could be used.

Ten years ago, Johnson Recovery purchased a wrecker for $400, 000 to move disabled 18-wheelers. He received a salvage value of $30, 000 after 10 years of use. During this 10-year period, his average annual revenue totaled $70, 000.

a) Did he recover his investment at 12% per year return? In other words, does the Annual Equivalent Value of the benefits exceed the Capital Recovery cost at an interest rate of 12%?

b) Suppose Johnson moves, on average, 150 disabled 18-wheelers each year. What is his average equivalent benefit/cost per vehicle moved?

c) Now, incorporate annual operating and maintenance costs into your analysis. If the annual O&M cost was $5, 000 the first year and increased by a constant 10% per year, is the AW positive or negative at 12% per year?

8. Brock Brothers wants to maintain its capital structure that consists of 30 percent debt and 70 percent equity. The company forecasts that its net income this year will be $1,000,000. The company follows a residual dividend policy and anticipates a dividend payout ratio of 40 percent. What is the size of the company's capital budget? a. $ 600,000 b. $ 857,143 c. $1,000,000 d. $1,428,571 e. $2,000,000 109. Makeover Inc. believes that at its current stock price of $16.00 the firm is undervalued in the market. Makeover plans to repurchase 2.4 million of its 20 million shares outstanding. The firm's managers expect that they can repurchase the entire 2.4 million shares at the expected equilibrium price after repurchase. The firm's current earnings are $44 million. If management's assumptions hold, what is the expected per-share market price after repurchase? a. $16.00 b. $17.26 c. $18.18 d. $20.00 e. $24.40 110. Myron Gordon and John Lintner believe that the required return on equity increases as the dividend payout ratio is decreased. Their argument is based on the assumption that a. Investors are indifferent between dividends and capital gains. b. Investors require that the dividend yield and capital gains yield equal a constant. c. Capital gains are taxed at a higher rate than dividends. d. Investors view dividends as being less risky than potential future capital gains. e. Investors value a dollar of expected capital gains more highly than a dollar of expected dividends because of the lower tax rate on capital gains. 111. Which of the following statements is most correct? a. In general, stock repurchases are taxed the same way as dividends. b. One nice feature of dividend reinvestment plans is that they enable investors to reduce the taxes paid on their dividends. c. On average, companies send a negative signal to the marketplace when they announce an increase in their dividend. d. If a company is interested in issuing new equity capital, a new stock dividend reinvestment plan probably makes more sense than an open market dividend reinvestment plan. e. Statements b and d are correct. 112. In the real world, we find that dividends a. Usually exhibit greater stability than earnings. b. Fluctuate more widely than earnings. c. Tend to be a lower percentage of earnings for mature firms. d. Are usually changed every year to reflect earnings changes. e. Are usually set as a fixed percentage of earnings. 113. A decrease in a firm's willingness to pay dividends is likely to result from an increase in its a. Earnings stability. b. Access to capital markets. c. Profitable investment opportunities. d. Collection of accounts receivable. e. Stock price. 114. Which of the f

Consider the Australian economy in 2017. At this time Australia economic growth was primarily being driven by a mining boom built on China's demand for Australian coal and iron ore. Assume that the Australia economy can be represented using a 4-sector multiplier model and the following hypothetical information: (All amounts are expressed in $m) c0 = 700, I = 1,500, G = 2,000, X = 1,200, c1 = 0.7, t = 0.15 and m = 0.095 a) What is the equation for aggregate demand (AD) in the Australian economy in 2017? (2 marks) b) Calculate the equilibrium value of income (GDP) in the Australian economy in 2017 and represent this on a fully labelled multiplier model diagram. Label all relevant axes, axis-intercept points, equilibrium points and curves on your graph. (4 marks) c) Assume that in 2018 the Australian economy experiences a decrease in demand for its coal from China due to a trade war between these two countries so that in 2018 the value of Australian exports is $1,000m. Write down the equation for AD in the Australian economy in 2018 and calculate the level of equilibrium GDP in 2018. (3 marks) d) Represent the situation described in c) in a multiplier model diagram. Show on a diagram and describe in words, the first two rounds of the multiplier process following the decrease in export spending. Include in your answer the relevant calculations for these two rounds of the multiplier process. (8 marks) e) What was Australian government's budget outcome for 2017 and 2018? Has the Australian government's budget position improved, deteriorated or not changed between 2017 and 2018.

Ram's Furniture Company makes only three kinds of furnitures (chairs, desks and tables). Each product requires some labor in the parts fabrication department, the assembly department and the shipping department. The furniture is sold through a local distributor who has Estimated the maximum potential sales for each product in the next quarter. Finally, the accounting department has provided some data showing the profit contributions on each product. The decision problem is to determine the product mix, that is, to maximise Ram's Furniture Company's profit for the quarter by choosing production quantities for the chairs, desks and tables. The table below summarises the parameters of the problems. Hours per Unit Department Chairs Desks Tables Hours Available Fabrication 4 6 2 1,850 Assembly 3 5 7 2,400 Shipping 3 2 4 1,500 Demand Potential 360 300 100 Profit $15 $24 $18

Q1: Using a spreadsheet model, determine the optimal solution that will generate maximum profits from current production.

Which of the following will not be a relevant factor when using the payback method of capital investment appraisal? (a) The timing of the first cash inflow (b) The total cash flows generated by the asset (c) The cash flows generated by the asset up to the payback period (d) The cost of the asset 11. Why the payback method is often considered inferior to discounted cash flow in capital investment appraisal? (a) I is more difficult to calculate (b) It does not calculate how long it will take to recoup the money invested (c) It does not take account of the time value of money (d) It only takes into account the future income of a project 12. Gross National Product is the total market value of all final goods and services produced in a year. (a) True (b) False 13. In 2005.......... was the least significant liability of U. S. nonfinancial businesses in terms of total value. (a) bonds and mortgages (b) bank loans (c) inventories (d) trade debt

What are the four key assumptions of the Lewis model that give rise to its conclusions? [8 marks] b) Describe four criticisms of Rostow's stages of economic growth theory. [12 marks] Question 4 a) "Science, technology and innovation hold the promise to ultimately achieving the Sustainable Development Goals (SDGs). Do you agree or disagree with this statement? Explain fully your reasoning. [15 marks] b) How does an increase in the savings rate affect economic growth? [5 marks] b) Describe fully how international bodies such as the IMF and the WB have promoted or encouraged a more market-oriented approach to growth in developing countries. Explain briefly why this is possibly problematic.

. Suppose that the production function is Q = L1/4K3/4. In the short-run, with capital held fixed at K = 256, a. Find the total product function. b. Find the average product of labour (AP) function. c. Find the marginal product of labour (MP) function. 1. b. i. The following is a general case of the Cobb-Douglas production function: Q = f(L, K) = AL K where A, and are positive constants. find the MRTS for this production function. ii. For A = 1, = 1/3 and = 2/3, find MRTS at bundles (1,216) and (64,27). Is MRTS diminishing? Show an isoquant diagram to depict the bundles and the MRTS (verify that both bundles are on the isoquant Q = 36). 2. Consider the same production function as in problem 1 (a), which is Q = L1/4K3/4 . a. For general w and r, derive the conditional input demand functions for L and K using the Lagrangian method. b. Find the combination of inputs that minimizes the cost of producing 1000 units of output for w = $1 and r = $4. c. Graph your result on a isoquant-isocost diagram. d. Is the demand for labour downward sloping? Is the demand for capital downward sloping? Use calculus to answer. 3. A paint manufacturing company has a production function Q = 2K + 2L1/2 . a. Use the Lagrangian method to derive the input demand functions for L and K for an interior optimum. b. What is the cost-minimizing input combination to produce 100 units of output if the firm faces input prices w= 1 and r =50? Draw an isoquant-isocost diagram and show your cost-minimizing bundle. c. Verify that the firm's cost-minimizing input combination to produce Q = 100 involves no use of capital when r = 110 keeping w = $1. What is the amount of labor the firm would use in this situation? d. In part ( c ), is MRTS equal to the input price ratio? If not, does it make sense that the equality is not satisfied at the optimal bundle?

3. A fixed cost is a cost which a. varies in total with changes in the level of activity b. remains constant per unit with changes in the level of activity c. varies inversely in total with changes in the level of activity d. remains constant in total with changes in the level of activity 4. Cost behavior analysis is a study of how a firm's costs a. relate to competitors' costs b. relate to general price level changes c. respond to changes in activity levels within the company d. respond to changes in the gross national product 5. Cost behavior analysis applies to a. retailers b. wholesalers c. manufacturers d. all entities 6. The relevant range of activity refers to the a. geographical areas where the company plans to operate b. activity level where all costs are curvilinear c. levels of activity over which the company expects to operate d. level of activity where all costs are constant 7. Which of the following is not a plausible explanation of why variable costs often behave in a curvilinear fashion? a. Labor specialization b. Overtime wages c. Total variable costs are constant within the relevant range d. Availability of quantity discounts 8. Firms operating constantly at 100% capacity a. are common b. are the exception rather than the rule c. have no fixed costs d. have no variable costs

Assume that the markets for sugar cane, rum and whiskey are initially in equilibrium (i.e., supply equals demand in each case). Assume further that a good harvest impacts the world's sugar cane crop. Sugar cane is a principal ingredient in rum, but it is not an ingredient in whiskey. Rum and whiskey are substitutes in consumption. (i) Discuss the impact of the good harvest on each of the three markets. (ii) Discuss the effect on the markets for each of the three products if the government implements a price restriction in the sugar cane market with the aim of protecting the farmers. How will this impact the revenues for sugar growers, rum producers, and whiskey producers? (b) Identify a newspaper article that illustrates a market failure in your assigned Caribbean country. Ensure that you provide a screenshot of the article in your submission. NOTE: Only the following market failures should be examined: public good, asymmetric information, positive or negative externality. (i) Provide a brief summary of the main points in the article. (ii)Identify the type of market failure being discussed in the article and discuss why market failure occurs in this scenario. (iii) Suggest a relevant government policy that would yield the efficient outcome and carefully explain the process through which the implementation of the government policy will lead to the optimal outcome. (iv) How will the imposition of the chosen government policy impact consumer surplus, producer surplus, and total surplus in this scenario?

You are the actuary to a large UK defined benefit pension scheme which provides a range of pensions and life assurance benefits. The employer currently contributes 20% of salaries to this scheme and members contribute at the rate of 5%. The Human Resource (HR) director has approached you and suggested that as employees do not appreciate the pensions package, the value of this is to be notified to them as part of the annual exercise which informs them of their salary increase. (i) Outline the points to be included in a letter to the HR director explaining why it would not be appropriate for the value notified to employees to be the rate of contribution currently being paid by the employer to the scheme. [8] (ii) It is decided to use an approach which expresses the cost as a percentage of the employee s salary, the relevant percentage is age-related. Discuss the issues to be considered in setting the assumptions to be used to determine the relevant table of percentage rates. [18] (iii) Describe two alternative approaches of establishing the value to be shown and list any particular problems that these could give rise to. [6] (iv) Five years later, you are asked to draft a letter responding to a member who has complained. Based on the information supplied on his annual statements, the member was expecting his pension benefits to have a current value of 70% of his salary, whereas the transfer value he has been offered as an alternative to his deferred benefits is approximately half of this amount. Outline the points to be included in the letter. [7] (v) Having read the reply, the member responds that he has approached a financial adviser who has told him that the transfer value offered is only sufficient to buy a deferred annuity of one-third of the scheme deferred pension. Outline the points to be included in the reply to this subsequent letter