If your utility function is the following form: U(c) = c1 + B c2, where c1 is the consumption in period 1, c2 is the consumption in period 2, the time-preference parameter, B= 1 and period 1's endowments el= 500 and period 2's endowments e2 = 400, what is the optima consumption in each period if (a) the interest rate (r) is zero, and (b) the interest rate (r) is positive?
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- The set-up remains deterministic (i.e., no uncertainty) and has two periods. c is period 1 consumption and c' is period 2 consumption. S is savings, w is wealth, and r is the return on saving. max [w.r.t c, S] {U(c) + W (c') subject to - c + S <= w c' <= (1 + r)S Inada conditions hold max [ w.r.t S] {U(w - S) + W (S(1 + r))} (a) Solve for optimal savings as a function of r and w. (b) Assuming W = W (c) = U(c) = c^1-γ / (1-γ), γ >= 0, solve for ∂S/∂r and show that if γ f γ > 1, ∂S/∂r < 0; if γ = 1, ∂S/∂r = 0 (c)Try to explain intuitively what these results in (b)Suppose Real Option Inc. has a product that generates the following cash flow. At t=1, the demand can be high or low. There is a probability of 0.6 that demand is high. If demand is high (low) the cash flow is CFH=400 (CFL=200). At t=2, the demand can also be high or low. If demand was high at t=1, then a high demand at t=2 arises with probability 0.7. If demand was low at t=1, then a high demand at t=2 arises with probability 0.2. If demand is high (low) at t=2 then CFH=400 (CFL=200). The interest rate for this project is 20%. (a) Draw the event and decision tree. (b) What is the market price (expected value) of Real Option Inc. at t=0? Now suppose Real Option Inc. can rent a platform to run a marketing campaign. For this purpose Real Option Inc. must sign a two year contract with the platform provider. The costs for using the platform are 180 per period. Marketing itself does not cost anything and has the following effect. In the high demand state, marketing doubles the demand. In…John and Peter are two representative consumers/investors who maximize the utility of consumption. John's utility of consumption is characterized as ln(x) + 2ln(y) while Peter puts more weight on the current consumption level and has a utility function of 2ln(x) + ln(y). John has a wealth of ($10, $20) thousand, while Peter has a wealth of ($20, $15) thousand now and next year, respectively. (a) What are the optimal consumption plans forJohn and Peter,respectively,if the interest rate is 5% per annum? (b) If John and Peter are the only investors/consumers, what is the equilibrium interest rate? (c) Further to part (b), how much do they borrow or lend to each other?
- An individual’s utility function is given as U (X) = X 0.5 where X represents the money, he has available for spending in a given time period. This individual has income of $225 in each time period and he discounts the future at the rate of 0.7. If he invests his up-front cost is 25 and his return in in the next time period is 35. a. Would this individual consider investing if his investment is financed by borrowing and cost of borrowing is 30%? (Consider two period model to justify your answer) b. Would this individual consider investing if his investment is financed by current savings? (Use two period model to justify your answer). c. Would this individual consider investing if his investment is financed by: $10 from current savings and rest of it from borrowing and the cost of borrowing is 30%? (Use two period model to justify your answer).Q1. A real-estate investor has the opportunity to purchase a small apartment complex. The apartment complex costs $4 million and is expected to generate net revenue (net after all operating and finance costs) of $60,000 per month. Of course, the revenue could vary because the occupancy rate is uncertain. Considering the uncertainty, the revenue could vary from a low of − $10,000 to a high of $100,000 per month. Assume that the investor’ s objective is to maximize the value of the investment at the end of 10 years.a) Do you think the investor should buy the apartment complex or invest the $4 million in a 10-year certificate of deposit earning 9.5%? Why? b)b) The city council is currently considering an application to rezone a nearby empty parcel of land. The owner of that land wants to build a small electronics-assembly plant. The proposed plant does not really conflict with the city’s overall land use plan, but it may have a substantial long-term negative effect on the value of the…An investor has $24,000 to invest in bonds of AAA and B qualities. The AAA bonds yield an average of 6% and the B bonds yield 10%. The investor requires that at least three times as much money should be invested in AAA bonds as in B bonds. How much should be invested in each type of bond to maximize the return? What is the maximum return? Define the variables needed to solve this problem. Organize your given information. (This part NOT graded, but encouraged.) Write the complete linear programming problem, which includes the objective function and all constraints. Graph and make sure all lines are labeled and shaded/solution region is clear and easy to identify. Create a corner point chart. Remember to mark your solution. Answer in a complete sentence or two: How much should be invested in each type of bond to maximize the return? What is the maximum return?
- Provide an example of a real-world application in finance or economics where bounded summation is used to calculate the present value of future cash flows.Suppose that you plan to retire at 65. You invest $8,000 per year on your birthday for 10 years starting on your 25th and ending on your 34th birthday. Since you are young, you take more risks with your investments, and earn a rate of return of 12%. Then, you have children and decide to put all your retirement savings into investing in a college fund for them. You leave all accumulated funds in the retirement account, and it earns 6% per year, reflecting an (unwise) rise in caution during middle age. How much money will you have to retire on at 65 (31 years after you stop contributing)select the correct answer from the options bellow: statement1 : A steep negative slope of a line in a sencitivity graf indicates that the NPW is not sencitive to change in the value of the corresponding variable. statement2: A scenario in the "scenario analysis "approach can only be one of three scenarios cases :the base case , the best case , and the worst case. (a) statement 1 and 2 are both false (b) statement 1 and 2 are both true (c) statement 1 is false but statement 2 is true (d) statement 1 is true but statement 2 is false
- The more risky future options or alternatives are a) the less rational people will necessarily be. b) the more future values must be discounted to obtain their present values. c) the greater their present values. d) the greater their net values in the future.Clare is contemplating her possible consumption patter for this year and next. She know that she will have income of $50,000 this year and $55,000 next yea. Her plan is to consume $40,000 this year (t=0). She is also going to invest 30,000. This investment has a positive NPV of $450. She decides to take the investment; in addition, the return on the investment is 9.62%. What consumption she can expect at t=1? (show a detailed procedure)An aggressive investment in Industry 4.0 next-generation technology has the potential to save your company $7M if it is very successful, or $3M if it is moderately successful, but it will cost $2M if it fails. The relative risk for the project is $1.25M. The company has a risk tolerance of $1 million and has assigned a utility value of .777 based on an exponential utility function for this investment. What is the value of a safe investment that the company would just as soon choose rather than investing in the IT project? A. $2M B. $1.5M C. 52.75 D. $1.25M