Clearly elaborate your answer.
1.Suppose the economy begins in a long-run equilibrium.
a.Draw the AD-AS model in its long-run equilibrium, E1.
b.Draw the money market in its initial equilibrium, E1.
c.Suppose there is a spike in housing prices, (note that houses are a major source of wealth for American consumers). Draw the effect on your AD-AS diagram in part a, labelling the new equilibrium E2. State the effect on prices and GDP. Are we in a recession or a boom?
d.The Federal Reserve is concerned about rising inflation and wants to prevent it from getting any higher. To fix this, will they increase or decrease the money supply?How exactly do they responded to you
e.Draw this change in the money supply on your money market diagram in part b, labelling the new equilibrium E2. What is the effect on interest rates?
f.What effect does this change in the interest rate have on the macroeconomy? Why? Draw this impact on yourAD-AS diagram in part a.State how prices and GDP change.
g.In the long-run, how does this change in prices and GDP affect the interest rate? Explain in words and draw on your money market diagram in part d....
Question 1 continued 2. Consider now the non-trivial case r(p', w') # r(p, w). Rewrite (p'-p).(x(p,w) - a(p, w)) = p(x(p',w) - r(p,w))-p-(x(p, w') - a(p. w)) . Consider separately each term of the right-hand side. Derive the signs of each of the two terms using (some) assumptions of the proposition and the fact that we assumed w' = p' - x(p,w) for the compensated law of demand. To derive the sign of the second term of the right-hand side you will need to make use of the weak axiom of revealed preference. 3. Put everything together to conclude the proof of the first direction. c.) Given the characterization of the compensated law of demand by the weak axiom of revealed preference, you need to explain to your grandmother the meaning of the weak axiom of revealed preference. Provide a verbal interpretation of the weak axiom of revealed preference. d.) The weak axiom of revealed preference may be viewed as a condition on the "con- sistency of consumer choice". We may be inclined to label a consumer violating this condition as being "irrational" (unless a more complex setting is considered). So the above proposition characterizes the compensated law of demand in terms of consistency of consumer choice. But is it really a characterization in terms of rational consumer choice in the sense of having complete and transitive preferences over consumption bundles? That is, is the following conjecture true? Conjecture: Suppose that the Walrasian demand function r(p, w) is homoge- neous of degree zero and satisfies Walras' law. Then r(p, w) satisfies the com- pensated law of demand if and only if the consumer has complete and transitive preferences over consumption bundles. Consider both directions of the conjecture separately. Moreover, consider the spe- cial case of L = 2 separately. (You don't have to present a detailed proof. You can make use of results learned in class. The line of arguments should be clear.)Question 1 [40 marks[ Norman Company has an opportunity to produce and sell a revolutionary new smoke detector for homes, and the project would expect to last for 6 years. To determine whether this would be a protable venture, the company has gathered the following data on probable costs and market potential: 1. New equipment would have to be acquired to produce the smoke detector. The equipment would cost $600,000 and be usable for 6 years. After 6 years, it would have a resale value at $60,000. Over the 6-year period, annual depreciation would be $90,000. 2. Production and sales of the smoke detector would require a working capital investment of $120,000 to nance account receivable, inventories, and day-to-day cash needs. This working capital will be locked for the whole project duration, and would only be released for use elsewhere after 6 years. 3. An extensive marketing study projects sales in units over the next 6 years as follows: 4. The smoke detectors would sell for $60 each, and total variable costs would be $32 per unit. 5. The company is required to advertise heavily during the early years of sales. The advertising program follows: 120,000 60,000 l 2 W 4-6 20,000 6. Annual xed costs (excluding depreciation indicated in 1. above) for salaries, insurance etc would totaled $110,000 per year. 7. The equipment would need a major repair at the end of year 4, and would cost $70,000 to do so. 8. The company's required rate of return is 18%. 9. Income tax is ignored for the analysis. Required: 1. How should depreciation and its associated income taxes be treated in capital budgeting analysis? Explain. (4 marks) Compute the net cash inow (cash receipts less yearly cash operating expenses) anticipated from sale of the smoke detectors for each year over the next 6 years. Initial acquisition of equipment and investment in working capital should be IGNORED in this part. (6 marks) Using the data computed in (2) above and other data provided in the question, determine the net present value of the proposed investment. Would you recommend that Norman Company accept the smoke detector as a new product? (14 marks) Is the project's internal rate of return higher or lower than 18%? (2 marks) For this part, assuming all annual cash ows happen evenly over the years (for simplicity, assuming resale of equipment and release of working capital at the end of year 6 will also be happening evenly over year 6): a. Calculate the payback period for the smoke detector project (4 marks) b. Calculate the discounted payback period for the smoke detector project (6 marks) Discuss the pros and cons of using payback method. (4 marks) Problem 1: Risk and Expected Utility lI'Llonsider aperson with a current wealth \""0 = 101}, EH31] who faces the prospect of p = .25 chance of losing; 211.000 through car theft during the next year. Suppose that his utility function is UHF} = an where W is the person's wealth at the end of the year. This person can buy an antitheFt device that costs $1.95!} and reduces the probability of the to p' = {1.15. {a} 1Will this person buy the antithcft device? Show mathematically why this is the case. Now suppose there is an insurance company that sells full insurance coverage. The premium is determined as the actuarially fair premium plus $200 of admin- istrative charges. The company cannot monitor whether or not the individual installed a device. so the probability of theft used by the insurance company to determine the premium is p = .25. {b} What premium does the insurer charge? Does the consumer buy insurance? Does the consumer buy the device? Show how you de- termine this. Assume now that the insurance company can monitor whether or not the in- dividual installed an anti-theft device and charge a premium based on whether consumer uses the device or not. If a consumer doesn't use the device+ the pre- mium is the actuarial fair price {for p = .25} plus $21110 to cover administrative costs. If a Consumer does use the device1 the premium will he the actuarially fair premium [for p' = .15] plus $2M] of administrative charges and an additional $1ll to cover the monitoring masts [the cost of verifying that the consumer is using the device]. Assume that the insurer does not cover the cost cl buying the device and does not cover theft of the device itself (Le. the insurer only covers the less of El]. (c) How mud: does insurance cost with and without the device installed? What will the individual do? Will the individual install an antithett device? Will he buy insurance? What type of insurance will the person hay: with or without anti-theft device
