4. The Best Elect electronics store is having a sale on November 8th on any new electronics purchased. Every customer will receive $50 off their purchase of a new electronic item. They are also offering a student discount on every item in the store for the whole month of November. If you can prove you are a student, you will receive 15% off any item. Let x be the price of any new electronic item in the store. a. Write a function P(x) that represents the price of a new electronic item on November 8th for any customer. b. Write a function D(x) that represents the price you will pay for an item after the student discount is applied during any day in November.
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- An investment club has set a goal of earning 15% on the money it invests in stocks. The members are considering purchasing three possible stocks, with their cost per share (in dollars) and their projected growth per share (in dollars) summarized in the following table. (Let x = computer shares, y = utility shares, and z = retail shares.) Stocks Computer (x) Utility (y) Retail (z) Cost/share 30 44 26 Growth/share 6.00 6.00 2.40 (a) If they have $392,000 to invest, how many shares of each stock should they buy to meet their goal? (If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (x, y, z) = ? (b) If they buy 700 shares of retail stock, how many shares of the other stocks should they buy? computer ? shares utility ? shares What if they buy 1400 shares of retail stock? computer ? shares utility ? shares (c) What is the minimum number of shares of computer stock they should buy?? sharesWhat is the…Let PX denote the price of product X (and likewise for other subscripts); M, the consumers’ income, and AX, the amount invested in advertising for product X (and likewise for other subscripts). If PY = 6; AZ = 50000; PW = 0.5, when graphing the demand function QDX = 3500 – 250PX – 280PY – 0.02AZ, what is the intercept of the Q-axis? Select one below. (A) 566.7667. (B)-13. (C) 820. (D)1050. 2. Imagine the market for Good X has a demand function of QDX = 40 – PX and a supply function of QSX = 2PX – 20. Suppose the current price of Good X (PX) is 30. Calculate consumer surplus (CS). CS = ________ 3. Imagine the tea market has a demand function of QDX = 10 – 2PX and a supply function of QSX = PX − 2, where PX is the price of the tea. Assuming the price is at equilibrium, calculate the equilibrium price (P*). P* = _________ 4. MacGuffins have a demand function of QD = 70 – P and a supply function of QS = 2P + 10. Determine the price at equilibrium PS = _______ 5.…Suppose Martha earns an of income 400 Birr currently, and her utility function is given by: U(m) = 4m, where m represents income. She has two options: Option 1: to buy a share. If she is successful her income will be 700 Birr and if she is not successful her income will be 100 Birr. Option 2: to do nothing and keep on earning 400 Birr. Assuming that success and failure are equally likely, a) What would be her expected income if she buys the share? b) What would be her expected utility of buying the share? c) Would Martha buy the share? Why? and Is Martha risk averse, risk lover or risk neutral?
- Q1. A farmer believes there is a 50-50 chance that the next growing season will be abnormally rainy. His expected utility function has the form Expected utility = 0.5lnYNR + 0.5lnYR Where and represent the farmers income in the state of ‘normal rain’ and ‘rainy’ respectively. Suppose the farmer must choose between two crops that promise the following income prospects Crop YNR YR Wheat $83,000 $10,000 Maize $83,000 $15000 What mix of wheat and maize would provide maximum expected utility to this farmer?3. 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?Suppose you are considering whether to purchase a house off of Lake Erie for $400,000. You expect thetotal costs of maintaining the property (utilities, repairs, etc.) to equal $15,000/year, and that you would be able togenerate $35,000/year in revenue if you were to put the house on the short term rental market.a. (3) Suppose you are deciding between purchasing the home or whether to invest $400,000 in an interest-bearingaccount. If your objective is to maximize your own net income, what would the interest rate have to equal for youto invest in the interest-bearing account?b. (4) Suppose you decide to buy the house, and now you have to decide whether/when to list the house on theshort term rental market (like Airbnb) or stay in the house yourself. Briefly explain what this decision woulddepend on. What are the implicit (opportunity) costs associated with renting the house to someone else on a givenday? What are the implicit costs associated with the staying in the house yourself?c.…
- Seung's utility function is given by U - C^(1/2), where C is consumption and C^(1/2) is the square root of consumption. She makes $50,625 per year and enjoys jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $30,000, and lose an additional $5,000 from missing work. a. What is Seung's expected utility without insurance? b. Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is the expected utility if she buys it? Policy cost: $___ Expected utility: ___ c. Suppose Seung can buy insurance that will cover her medical expenses and foregone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it? Policy cost: $___ Expected Utility: ___(a) The sales of a book publication are expected to grow according to the functionS = 300000(1 − e−0.06t), where t is the time, given in days.(i) Show using differentiation that the sales never attains an exact maximum value.(ii) What is the limiting value approached by the sales function?(b) A poll commissioned by a politician estimates that t days after he makes a statementdenegrating women,the percentage of his constituency (those who support him at the time hemade the statement) that still supports him is given by S(t) =75(t2 − 3t + 25)t2 + 3t + 25The election is 10 days after he made the statement.(i) If the derivative S’(t) may be thought of as an approval rate, derivate the a functionfor his approval rate.(ii) When was his support at its lowest level?(iii) What was his minimum support level?(iv) Was the approval rate positive or negative on the date of the election?(c) Lara offers 100 autograph bats. If each is priced at p dollars, it is that the demand curvefor the bast will be…64. (This problem assumes knowledge of the basic rulesof baseball.) George Lindsey (1959) looked at boxscores of more than 1000 baseball games and foundthe expected number of runs scored in an inning foreach on-base and out situation to be as listed in the fileP09_64.xlsx. For example, if a team has a man on firstbase with one out, it scores 0.5 run on average untilthe end of the inning. You can assume throughout thisproblem that the team batting wants to maximize theexpected number of runs scored in the inning.a. Use this data to explain why, in most cases,bunting with a man on first base and no outs isa bad decision. In what situation might buntingwith a man on first base and no outs be a gooddecision?b. Assume there is a man on first base with one out.What probability of stealing second makes an attempted steal a good idea?
- Prospect Y = ($6, 0.25 ; $15, 0.75) If Will's utility of wealth function is given by u(x)=x0.25, what is the value of CE(Y) for Will? (In other words, what is Will's certainty equivalent for prospect Y?) (The certainty equivalent represents the maximum amount a person would be willing to pay to acquire a risky prospect, and equivalently, the lowest price for which they would be willing to sell a risky prospect if they already owned it) (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)Mr Usu has an expected utility function with u(x) = x0.5. He is analyzing an investment opportunity that promises to pay out $1,160 with prob. 0.6 and $2,800 with prob. 0.4. What is the expected utility of this opportunity?Suppose that instead Einar short sells 200 shares of German Power Weak Inc. at $40 each. NASDUCK now sets a margin requirement of 30%.(e) How much cash does Einar need to invest?(f) Calculate the margin call of NASDUCK if the price increases to $44.(g) Suppose the price falls to $25. How much cash can Einar take out from his margin account?(h) Suppose he takes out 50% of the amount in part (g). At what price threshold will Einar face a margin call by NASDUCK?