Consider the model of investment under asymmetric information D=(1 + r)(1- W). Suppose that initially the entrepreneur is undertaking the project, and that (1 + r)(1- W) is strictly less than RMAX. Describe how each of the following affects D:
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Consider the model of investment under asymmetric information D=(1 + r)(1- W). Suppose that initially the entrepreneur is undertaking the project, and that (1 + r)(1- W) is strictly less than RMAX. Describe how each of the following affects D:
(a) A small increase in W .
(b) A small increase in r.
(c) A small increase in c.
(d) Instead of being distributed uniformly on [0, 2γ], the output of the project is distributed uniformly on [γ - b, γ + b], and there is a small increase in b.
(e) Instead of being distributed uniformly on [0, 2γ], the output of the project is
distributed uniformly on [b, 2γ + b], and there is a small increase in b.
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- 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…In an intertemporal optimizing model consumption, a consumer living from time zero (0) to time t has a longer utility: U (C)= ln C. The market interest rate is r and the consumer is assuming no inheritance. Derive the consumption relationship and the marginal utilities between two adjacent periods. Using a diagram, explain the time profiles of paths based on (i) above. Show that consumption is proportional to the present value of future income at time zero (0) at a given interest rate.
- SM 3. Consider the problem of Example 12.4.2. (a) Suppose that Q=f(L) = √L. Write down Eq. (*) in this case and find an explicit expression for L* as a function of P and w. Find the partial derivatives of L* w.r.t. P and w. Then verify the signs obtained in the example. (b) Suppose the profit function is replaced by л(L) = Pf (L) – C(L, w), where C(L, w) is the "cost function". What is the first-order condition for L* to be optimal in this case? Find the partial derivatives of L* w.r.t. P and w.Consider the Consumption and Savings model with random future income. The utility function of the individual is: u(C0, C1) = (C0) + (C1)1/2, where C0 is present consumption expenditure and C1 is future consumption. Let the present income be $5, the interest rate in the financial market r = 5%, and the probability distribution of future income Y1 = (1, 2; 1/2 , 1/2). Calculate the expected utility of saving $0 (consume $5 in the present) (use two decimals)Q2: Consider a person who is thinking about whether to engage in a life of crime. He knows that, if he gets caught, he will be in jail and his consumption will be low, xº, but if he does not get caught, he will be able to consume an amount x₁ that is considerably above Χρ· (a) Suppose that x₁ = 20; x₁ = 80 (where both are expressed in thousands of pounds) and suppose the probability of getting caught is 8 = 0.5. What is the expected consumption level if the life of crime is chosen? (b) Suppose the potential criminal's tastes over gambles can be expressed using the following utility function u(x) = In (x). Calculate the person's expected utility from a life of crime. How does it compare with the utility of the expected value of consumption? Based on your answer, explain this individual's attitude towards risk and draw the consumption/utility relationship. (c) Consider the level of consumption this person could attain by not engaging in a life of crime. What level of consumption from an…
- A company has established that the relationship between the sales price for one of its products and the quanlity sokld per month is approximalely p=75-0. 1D (D is the demand or quantity sold per month and p is the price in dollars). The fixed cost is $1,000 per month and the variable cost is $30 per unit produced. a. What is the maximum profit per month for this product? b. What is the range of profitable demand during a month? a. The maximum profit per month for this product is $. (Round to the nearest dollar.) b. The range of profitable demand during a month is from units to units. (Round up the lower limit and down the upper limit to the nearest whole number.)Let X be a Bernoulli random variable. Which one of the following is true about 1 – E(X)? 1- Е(X) — Pr(X — 0) а. b. 1 - Е(X) — Var(X) 1- E(X) = Pr(X = 1) d. 1- E(X) = 0 С.(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…
- 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?Suppose that private savings and investment functions are given by: S = −c0 + (1 − c1)(Y − T) I = b0 + b1Y with G = T = 0. Assume 0 < b1 < 1−c1 < 1 (i.e. that slope of the savings curve is steeper than that of the investment curve). (a) Model Basics: Draw a graph of the investment=savings model with S,I on the vertical axis, and Y on the horizontal axis. Clearly label the 1) specific values of each intercept, 2) specific values of the slopes of each curve. (b) Suppose consumers choose to save more by reducing consumption at any given level of income, so that c0 declines. Show this on the graph. What are the effects of this change on 1) output, 2) the level of private savings, 3) the level of investment. (c) Briefly describe the economic intuition behind your results. Why is this called the paradox of thrift? (1-2 sentences is fine). (d) Deriving the Model: Show that the equilibrium condition Y = C + I + G implies I = S + T − GRefer the economic clock as time is 3:30 and you are required to [Marks invest in a real estate project with break-even on investment (return of investment) within 18 months of project start. Based on the data given below in which neighbourhood would you propose a project? What type of project? What would be your ideal investment size? Give justification to your proposed strategy.