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ECON 310: Problem Set #3 Please submit through Canvas Due Date: October 23, 2020 For all of the questions in this problem set, amume there is no tax at all. Stocks Consider stock A with a dividend yield equal to 2.5% (based on its dividend payments over the past year). The dividends are expected to grow at 8% per year. Stock A is currently traded at $52 per share. 1. According to Gordon's model, what would be the expected return on the stock? Answer: The Gordon's model states that 1+9 P = DI TE - 9 Rearrange the terms we get Pi(1+g) +9 = 2.5% . (1 +8%) + 8% = 10.7%% 2. Suppose the total dividends paid over the next year is $1.4 per share, leading to a downward revision of the expected dividend growth rate to 7.5%%, Assume the expected rate of return remains the same for this stock, what would be the actual rate of return from holding this stock over the next year? Answer: The price of stock A a year from now, according to Gordon's model, is 1+4 -14- 1+7.5% 10.7% -7:5%% =$47.03/share The rate of return is Rut - De + An -A 14+ 47.03-52 52 =-6.87% 3. Consider stock B which just paid $6 in dividends over the past year. The expected return on the stock is 12.5% and the stock is currently traded at $120 per share. At what rate are the dividends expected to grow for this stock according to Gordon's model? Answer: Again, starting with the Gordon's model 1+9 PEDITE - 9 and rearrange the terms we have Pi(TE - 9) = Di(1+ 9)c. Graph an indifference curve that shows the bun- e. Connect the dots to create Josd's budget con- dles of X and Y for which U = 6 and U = 8. Is straint. What is the slope of the budget constraint? the "more is better" assumption satisfied for X f. Divide the price of fireworks by the price of and Y? music. Have you seen this number before while 7. Kelly's utility function is given by U= 3X + 21, working on this problem, and if so, where? where MU, = 3 and MU, = 2. R. Suppose that a holiday bonus raises Jose's in- a What is MRS ,? come temporarily to $360. Draw Jose's new b. What is MRS,, when X = 1 and Y - 57 When budget constraint. X = 2 and Y = 2.57 h. Indicate the new bundles of music and fireworks c. Draw a sample indifference curve. that are feasible, given Jose's new income. 8. Andrea loves to eat burritos with hot sauce, In fact, 1 1. Suppose that only one person in the world sells ice she cannot enjoy a bumto (8) unless it has three cream. She employs a strange pricing policy: You can servings of hot sauce (H ). She gets no additional en- buy I ice cream cone for $1, but if you buy 2 cones, joyment from more than three servings per burrito. you have to pay $2 each. If you buy 3. you have to Thus, her utility function is (= min [ B.- H ). Graph pay $3 each, cic., so that if you buy 10, you have Andrea's indifference curves for U= 1 and U= 2. to pay $10 each. You have $100 dollars to spend on ice 9. Suppose John's utility function is 4XY, where X is cream comes and chocolate milk, and chocolate milk consumption of beer and I is consumption of pizza. costs $1 per unit Draw your budget constraint. This For this utility function, the marginal utility of X is strange ice cream pricing, where buying more costs given by MU, = 41, the marginal utility of F is given you more, is called a quantity surcharge. by MU,= 4X. 12. John enjoys ordering out for pizza and renting mov- I Suppose Y= 3. Calculate John's utility for X - 2, ies online. He makes $30 each week at a part-time 3, 10, and I1. For a given level of Y, does good X job. If movies cost $2 per rental and pizza costs display diminishing marginal utility? $7.50 per slice. graph John's budget constraint. Then illustrate the effects of each of the following b. Suppose X - 3. Calculate John's utility for Y = 2. events; 3, 10, and 11. For s given level of X, does good F display diminishing marginal utility? a. John's mother finds a coupon good for one free pizza and gives it to John. C. Find three different bundles containing X and Y' that give John 48 wils of satisfaction. Plot the The company John rents movies from sponsors theme bundles and connect them with an indiffer. holiday weck promotion: Rent the first five move coe curve. What happens to the marginal rate ies at their regular price, and all movies after the of sbalitution between X and Y' as consumption of fifth are half off. X' increases? C. John's favorite plaza place increases the price of 4. Does the principle of diminishing MAS depend pizza from $7 50 to $10. on the diminishing marginal utility of X and 17 13. Good X sells for $4, and good F sells for $2. At your 10. Jose gets satisfaction from both music and fireworks. current level of consumption, the marginal rate of Jon's income is $340 per week. Music costs $12 per substitution between X and Fisd. CD, and fireworks cost $8 per bag. I Draw an indifference curve and budget constraint It Graph the budget constraint Jose faces, with that reflects the facts given above. (Mar: You music on the vertical axis and fireworks on the will have to choose an linkial income level and horizontal suit an initial bundle of X and F.) I Jost spends all his income on music, how b. Are you maximizing your utility? much music can be affordt Plod a point that c. If you are not maximizing your utility, are you illustrates this scenario, buying low much X or too much IT Explain. c.IT hard spends all his incommon fireworks, him 14. Andre gets utility from playing laver tag and read- many bags of fireworks can be afford? Plot a ing books. Each week. Andre spends his entire $100 point that Illustrates this scenario paycheck in both pools, One hour of laver rag cous If Joad spends half his income on fireworks and $30: s bick costs $10. half his income un music, how much of each a. Graph Andre's budget constraint. Put books on can be allland? Hot s point then illustrates this the horizontal axis and hour of laser tag on the vertical unit.GEST 1013 Mathematics in Modern Society Topic 3: Linear Correlation and Regression Analysis Assignment 3 Question 1 For the following data: X 3 4 6 8 9 11 14 V 1 2 4 4 5 7 8 9 Required: (a Draw a scatter diagram. (b) Find an equation of the line of best fit. (c) Estimate a value of y corresponding to x = 10. Question 2 As part of an investigation into levels of overtime working, a company decides to tabulate the number of orders received weekly and compare this with the total weekly overtime worked to give the following: Week 2 3 5 6 7 10 Number Orders 83 22 107 55 48 92 135 32 67 122 received Total 38 9 42 18 11 30 48 10 29 51 Overtime Hours Required: (a Find an equation of the line of best fit. Estimate total overtime hours necessary for 100 orders. (c) Given that normal weekly hours for an employee are currently 35, state in words what criterion is necessary for the company to consider taking on a new employee.Question 9 (Decision Rules) Suppose the budgeted demand for product X will be 11500 units if the price $10, 8500 units if the price is $12 and 5000 units if the price is $14. Variable costs are estimated at either $4, $5, or $6 per unit. A decision needs to be made on the price to be charged. Here is a contribution table showing the budgeted contribution for each of the nine possible outcomes: Demand Price Variable Cost Unit Total Contribution Contribution $ S 11500 10 69000 11500 10 57500 11500 10 46000 8500 12 68000 8500 12 59500 8500 12 51000 5000 14 50000 5000 14 45000 5000 14 40000 Required: State which price should be set using each of the decision rules: maximax, maximin and minimax regret criteria Question 10 (Decision Tree) A firm has developed a new product X. They can either test the market or abandon the product. The details are set out below: Test market cost $50000; likely outcomes are favourable (probability = 0.7) or failure (probability = 0.3). If favourable they could either abandon or produce it when demand is anticipated to be: Low Demand Probability = 0.25 Loss $100000 Medium Demand Probability = 0.6 Profit $150000 High Demand Probability = 0.15 Profit $450000 If the test market indicates failure the project would be abandoned. Abandonment at any stage results in a gain of $30000 from the special machinery used. Required: Draw the decision tree showing the possible cases with probabilities