Tim has preferences over consumption in period 1 and 2 of the form . The price...

Tim has preferences over consumption in period 1 and 2 of the form . The price of consumption is $1 in both periods. He has $10,000 in the bank now and is trying to decide between two different investment opportunities, A and B.

A: invest $4,000 in period 1 and receive $8,000 in period 2.

B: invest $2,000 in period 1 and receive $5,000 in period 2.

If Tim can borrow and save at a rate of interest of 50 percent, which investment opportunity will he choose? (Assume that Tim cannot invest more than $4000 if he chooses A, or $2000 if he chooses B.) Show your analysis

Given your answer in (a), how much will he consume in each period?

Given your answer in (a), how much will he consume in each period if now his saving interest rate is 20% and the borrowing rate is still 50%? Show your analysis.

Expert Solution

Underlying objective behind each investment is to maximize the Net Present Value (NPV). Using a discount rate of 50%, the NPVs of both the investments is:

1) NPV of A = - 4000 + 8000 / 1.5 = $ 1,333.33

2) NPV of B = - 2000 + 5000/1.5 = $ 1,333.33

SInce the NPV in both the cases is same, the next step would be to compare the rate of returns of two investments.

RoI for A = (8000 - 4000) / 4000 = 100 %

RoI for B = (5000 - 2000) / 2000 = 150 %

Tim will choose investment opportunity B because fir the same NPV, Tim receives higher RoI for investment B.

Tim will consume $ 2000 in period 1 and $ 4000 in period 2 because these investments provides higher returns than keeping the money in bank as the savings interest rate is 50%. Tim will be better off by investing $ 2000 in period 1 and $ 4000 in period 2.

The answers will still be the same if the interest rates change because Tim has enough money in bank and there is no need to borrow. Also there are limits on investment amounts ($ 4000 in A and $ 2000 in B).

jeff jeffy answered 8 months ago

1. (40 marks) Tim has preferences over consumption in period 0 and 1 of the form...

1. Tim has preferences over consumption in period 0 and 1 of the form U(x, y) = xy, where x and y are Tim’s consumption in period 0 and 1 respectively. He has $15,000 in the bank now and is trying to decide between two different investment opportunities, A and B. A: invest $10,000 in period 0 and receive $20,000 in period 1. B: invest $2,000 in period 0 and receive $6,000 in period 1. a. If Tim can borrow...

Problem 2: Consider a representative consumer whose preferences over consumption and leisure are given by the...

Problem 2: Consider a representative consumer whose preferences over consumption and leisure are given by the following utility function: U˜(C, l) = U(C) + V (l) (2) where U(.) and V (.) are twice differentiable functions (that is, their first and second derivatives exist). Suppose that this consumer faces lump-sum taxes, T, and receives dividend income, Π, from the 100% ownership of shares of the representative firm. A) Write down the consumer’s optimization problem and the first-order conditions determining optimal...

: Suppose that the representative consumer’s preferences over current consumption (C) and future consumption (C 0...

: Suppose that the representative consumer’s preferences over current consumption (C) and future consumption (C 0 ) are given by the following utility function U(C, C0 ) = CC0β The market real interest rate is denoted by r and β > 0. 1. Write down the consumers’ budget constraint for the current and future period. 2. Using the equations in part (1), obtain the inter-temporal budget constraint. 3. Set up the consumer’s optimization problem using the Lagrangian approach. Next, derive...

Consider a one period economy in which the representative consumer has preferences over leisure (l) and...

Consider a one period economy in which the representative consumer has preferences over leisure (l) and consumption (c) described by the utility function u(c, l) = c0.5l0.5 This consumer has 1 unit of time h to spend between leisure, l, and labor supply, Ns. The representative firm’s production function is Y = zNd where Nd is labor demand and z = 2 is total factor productivity. The government buys one unit of consumption good, meaning that, G = 1. (a)...

Priya has preferences over consumption and leisure given by U(C,L) = CL. Her total number of...

Priya has preferences over consumption and leisure given by U(C,L) = CL. Her total number of available hours in a given week is 100. Her non-labour income is £800. If she chooses to work, she earns w = £20 per hour. If the government starts a welfare policy that pays an amount of £B to all non-workers and pays 0 to all workers, at what value of B will Priya opt out of the labour force in order to go...

Barbara has preferences over flowers (x 1) and vases (x 2) represented by u( x 1...

Barbara has preferences over flowers (x 1) and vases (x 2) represented by u( x 1 , x 2 ) = x 1 x 2. Her income is m=100m = 100 and prices are initially p 1 = 1 and p 2 = 2. If the price of flowers increases to p 1 ′ = 5, the decrease in demand for vases attributed to the income effect is: 1. 0 2. 20 3. 50 4. 75

Ethel has preferences over amounts of goods 1 and 2 represented by the utility function u(x1,...

Ethel has preferences over amounts of goods 1 and 2 represented by the utility function u(x1, x2) = (x1)^2 + x2, where x1 denotes how much of good 1 she has and x2 denotes how much of good 2 she has. Write an expression for Ethel’s marginal utility for good 1. Does she like good 1? Explain your answer. Write an expression for Ethel’s marginal rate of substitution at any point. Do Ethel’s preferences exhibit diminishing marginal rate of substitution?...

Decomposition of the effect of a wage decrease on labour supply Bob’s preferences over consumption (c)...

Decomposition of the effect of a wage decrease on labour supply Bob’s preferences over consumption (c) and leisure (r) are represented by the following utility function: u(c, r) = c^(0.6)r^(0.4). Suppose that Bob is endowed with $100 and 50 hours (per week) to allocate between leisure and work. Denote the price of the consumption good by p and the wage by w. Express mathematically all the constraints faced by Bob. Draw Bob’s feasible set. Derive Bob’s (gross Marshallian) demands for...

Consider an individual with preferences defined over two goods, X1 and X2. This individual has preferences...

Consider an individual with preferences defined over two goods, X1 and X2. This individual has preferences that can be represented by the following utility function: u(X1, X2) = X1 + X 0.5 2 Let P1 = 4 and P2 = 2. In addition, suppose this individual has an income of $120. (a) Write down the expression for this consumer’s marginal rate of substitution of X1 for X2 (MRS12). Identify the distinguishing feature of this particular MRS12. (b) Calculate the optimal...

2. Consider a 1-period BOPM where a period is 1 year. The current stock price is...

2. Consider a 1-period BOPM where a period is 1 year. The current stock price is 40. The stock could up by 20% (u=1.2) or down by 10% (0.9) and the risk-free rate is 8%. The strike price of a call option is 45. What is the hedge ratio? 3. Consider a 1-period BOPM where a period is 1 year. The current stock price is 40. The stock could up by 20% (u=1.2) or down by 10% (d=.9) and the...

Question