You may need to use the appropriate appendix table or technology to answer this question. Suppose In 2018, RAND Corporation researchers found that 77% of all individuals ages 66 to 65 are adequately prepared financially for retirement, Many financial planners have expressed concern that a smaller percentage of those in this age group who did not complete high school are adequately prepared financially for retirement. (a) Develop appropriate hypotheses such that rejection of N, will support the conclusion that the proportion of those who are adequately prepared financially for retirement is smaller for people in the 66-69 age group who did not complete high school than it is for the population of the 66-69 year old. (Enter In for a as needed.} (b) In a random sample of 300 people from the 65-69 age group who did not complete high school, 159 were not prepared financially for retirement. What is the p- value for your hypothesis test? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = (c] At a = 0.01, what is your conclusion? Do not reject He. We conclude that the percentage of 66- to 69-year-old individuals who are adequately prepared financially for retirement is smaller for those who did not complete high school. Reject Ho. We conclude that the percentage of 66- to 69-year-old individuals who are adequately prepared financially for retirement is smaller for those who did not complete high school. Reject Ho. We cannot conclude that the percentage of 66- to 69-year-old individuals who are adequately prepared financially for retirement is smaller for those who did not complete high school. Do not reject H,. We cannot conclude that the percentage of 66- to 69-vear-old individuals who are adequately pranarad financially far vatican3. Consider the following delegation versus centralisation model of decision making, loosely based on some of the discussion in class. A principal wishes to implement a decision that has to be a number between 0 and 1; that is, a decision d needs to be implemented where 0 S d S 1. The difculty for the principal is that she does not know what decision is appropriate given the current state of the economy, but she would like to implement a decision that exactly equals what is required given the state of the economy. In other words, if the economy is in state s (where 0 S s s 1) the principal would like to implement a decision d = s as the principal's utility Up (or loss 'om the maximum possible prot) is given by UP = is d | . With such a utility mction, maximising utility really means making the loss as small as possible. For simplicity, the two possible levels of s are 0.4 and 0.7, and each occurs with probability 0.5. There are two division managers A and B who each have their own biases. Manager A always wants a decision of 0.4 to be implemented, and incurs a disutility UA that is increasing the further from 0.4 the decision d that is actually implement, specically, U A = 'OA d|. Similarly, Manager B always wants a decision of 0.7 to be implement, and incurs a disutility UB that is (linearly) increasing in the distance between 0.7 and the actually decision that is implemented - that is U B = |0.7 d l . Each manager is completely informed, so that each of them knows exactly what the state of the economy 5 is. 25. Characteristics of monopolistic competition include all of the following EXCEPT a. Barriers to entry b. A relatively large number of sellers and buyers C. Small market share for each seller d. Differentiated products and advertising 26. Which of the following industries is the best example of monopolistic competition? a. Cotton b. local utility c. automobiles d. service stations 27. A firm in monopolistic competition maximizes profits by producing the quantity where Marginal revenue equals marginal cost b. price equals marginal cost c. marginal revenue equals average cost d. price equals average cost 28. The monopolistic competitor faces a Horizontal demand curve b. vertical demand curve c. downward-sloping demand curve d. upward-sloping demand curve 29. If firms in monopolistically competitive industries are currently earning economic profits in the short run, then in the long run we can expect a. Economic losses to occur as too many firms try to enter the industry b. Firms to earn normal profits since new firms will enter the industry C. Economic profits to persist d. none of the above 30. One important difference between monopoly and monopolistic competition is the a. Slope of the demand curve that the industry faces b. free entry in monopolistic competition c. greater restriction of output in monopolistic competition d. coincidence of the marginal revenue and demand curves in monopoly 31. Under monopolistic competition a firm's ability to influence the price of the product it sells arises because a. Sellers in the market have large market shares b. Sellers in the market have small market shares c. The product of each seller is differentiated from that of others d. Each seller sells a standardized product 32. For which market structure will the firm shut down in the short run if it is not able to cover its variable cost (that is, its operating loss is grater than its fixed cost)? a. Perfect competition b. monopolistic competition c. monopoly d. all of the above 3. The monopolistic competitor produces the output at which a. Price equals marginal cost b. Marginal revenue equals marginal cost C. There is allocation efficiency d. Average total cost is a minimum The perfectly competitive firm charges a price while the monopolist charges a price a. Equal to marginal revenue; equal to marginal cost b. Equal to marginal cost; greater than marginal cost C. Equal to marginal revenue; greater than marginal revenue d. band c Some monopolistic competitors earn positive economic profits in the long run because There are high barriers to entry in monopolistic competition b. Some firms have successfully differentiated their products from their competitors' products C. There is easy entry and exit d. band c e. none of the aboveCASE 2 - COST STRCTURE and PRICING: Sting Ray PoolVac, Inc. manufactures and sells a single product called the "Sting Ray," which is a patent-protected automatic cleaning device for swimming pools. PoolVac's Sting Ray faces its closest competitor, Howard Industries, also selling a competing pool cleaner. Using the last 26 quarters of production and cost data, PoolVac wishes to estimate its average variable costs using the following quadratic specification: AVC =a+bQ+cq'. The quarterly data on average variable cost (AVC), and the quantity of Sting Rays produced and sold each quarter (Q) are presented in the data file. PoolVac also wishes to use its sales data for the last 26 quarters to estimate demand for its Sting Ray. Demand for Sting Rays is specified to be a linear function as the following: 0) = d + eP + fM + gPw. in which its price (P), average income for households in the U.S. that have swimming pools (M), and the price of the competing pool cleaner sold by Howard Industries (P,). QUESTIONS 1. Run the appropriate regression to estimate the average variable cost function (AVC) for Sting Rays. Evaluate the statistical significance of the three estimated parameters using a significance level of 5 percent. Be sure to comment on the algebraic signs of the three parameter estimates. (30%) 2. Given your answer in 1, show the estimated total variable cost, average variable cost, and marginal cost functions (7VC, AVC, and MC) for PoolVac. (15%) 3. Apply dummy variables to construct the time-series quarterly sales estimation of Sting Ray (Hint: Q = A+8+Dy...). Please predict the quantity sold in the first quarter 2014. (10%) 4. Run the log-linear regression to estimate the demand function for Sting Rays. Evaluate the statistical significance of the three estimated coefficients of parameters by using a significance level of 5 percent. Discuss the elasticities (price elasticity of demand, income elasticity and cross-price elasticity) to define the characters of Sting Ray. (20%) 5. The manager at PoolVac, Inc. believes Howard Industries is going to price its automatic pool cleaner at $250, and average household income in the U.S. is expected to be $65,000. Please run a multiple linear regression then explore the inverse demand function (i.e. Price is dependent variable) and marginal revenue (MR) function (Hint: Half-way rule). (15%) 6. Given your MC function in question 2 and MR function in question 5, what is the profit-maximizing unit price PoolVac should charge for Sting Ray? (Hint: Solve the quadratic equation by quadratic formula (10%) -btob - 4ac1. Derive the AD and AS relations. Consider the following economy: c=C+C1(Y_T) I=b+b1Y_b2i Government spending is given by G. The real money supply is MVP, and real money demand is given by doY/i. Suppose the wage is set according to W=P'(1au+z). The production function in this economy is given by Y = N, where N is employment, and labor force is given by L. The price of goods is set according to P = (1 + m)W Note that ha, b1, 132, cu, c1, do, a, m,z are positive constants. (a) Derive the IS relation. (b) Derive the LM relation. (c) Combining your results in (a) and (b), derive the AD relation. Explain Why it is called the AD (aggregate demand) relation. (d) Derive the AS relation. Explain why it is called the AS (aggregate supply) relation. (e) Solve the output in the medium run1 i.e., potential output Yn. (f) How does a monetary expansion affect Yn? How does a scal consolidation a'ect 1'\"? Do your results t the predictions from the examples in our lecture