What are the values of P, P2, Q1, Q2 given the two commodity demand and supply model: Qdi = 18 – 3P, +P2 Qn = -2 + 4P Qaz = 12 + P - 2Pz Q2 = -2 + 3P2 %3D %3D Select one: O a. P $3.47, P2 $3.09, Q1 11.4, Q2 7.32 O b. P $3.35, P2 $3.47, Q1 11.4, Q2 8.41 O. P $2.14, P2 $3.47, Q1 = 11.4, Q2 16.32 O d. P $3.59, P2 $1.86, Q1 16.32, Q2 1.18
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- Suppose that you have two opportunities to invest $1M. The first will increase the amount invested by 50% with a probability of 0.6 or decrease it with a probability of 0.4. The second will increase it by 5% for certain. You wish to split the $1M between the two opportunities. Let x be the amount invested in the first opportunity with (1-x) invested in the second. Find the optimal value of x. Using expected value as the criterion (linear utility) Using the flowing utility function: u(x)=2.3 ln〖(1+4.5x)Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person’s utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate δ = 0.05. Hence this person’s goal is to maximize 0ʃ40 e–0.05tu(c(t))dt = 0ʃ40 e–0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = – c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H = e–0.05t(c(t))0.5 + λ(– c(t)) + x(t)(dλ/dt). This person’s wine consumption decreases at a continuous rate of ??? percent per year. The number of bottles being consumed in the 30th year is approximately ???Suppose that there are only 10 individuals in the economy each with the following utility function over present and future consumption: U (c1, c2) = c1 +C2, where ci is consumption today, and c2 is consumption tomorrow. Consumption tomorrow is less valued because people are impatient and prefer consuming now rather than later. Buying 1 unit of consumption today costs $1 today and buying 1 unit of consumption tomorrow costs $1 tomorrow. All individuals have income of $10 dollars today and no income tomorrow (because they will be retired) but they can save at the market interest rater> 0. How much of his or her income will an individual consume today given that the interest rate is 0.3? O. Less than half of it O. Exactly half of it O. The individual is indifferent between consuming today and saving O. More than half of it O. All of it O. None of it How much of his or her income will an individual consume today given that the interest rate is 0.5? O. Less than half of it…
- A parent has two children named A and B and she loves both of them equally. She has a total of Php 1,000 to give them. How much will she give to each child given the different utility functions: a) U(a,b)= √a+√b b) U(a,b)=(−1/a) - (-1/b) c) U(a,b)=log(a)+log(b) d) U(a,b)=max(a,b) e) U(a,b)=min(a,b)If the consumer thinks that (x₁,x2) is at least as good as (y₁.42) and that (y₁y2) is at least as good as (x₁,x2), we can conclude that (look at the following options)‘‘Risk-averse people should only be averse to big gambles with a lot of money at stake. They should jump on any small gamble that is unfair in their favor.’’ Explain why this statement makes sense. Use a utility of income graph like Figure 4.1 to illustrate the statement. For a challenge, demonstrate the statement using a two-state graph like Figure 4.6.
- A woman with current wealth X has the opportunity to bet an amount on the occurrence of an event that she knows will occur with probability P. If she wagers W, she will received 2W, if the event occur and if it does not. Assume that the Bernoulli utility function takes the form u(x) = with r > 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA? Alex plays football for a local club in Kumasi. If he does not suffer any injury by the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coach worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = Assume he could buy insurance at price P that could pay $9,900 in case of injury. What is the highest value of P that makes it worthwhile for Alex to purchase insurance? What is the certainty…2. Tom spends all his $100 weekly income on two goods, apples and bananas. His utility function is given by U (A, B) = AB, where A and B stand for the quantity of apples and bananas consumed by Tom. If PA = $4 and PB= $10, how many apples and bananas will he consume? Make sure you write out the utility maximization problem explicitly, including the decision variable(s). What if his utility function is given by U (A, B) = A0.5B 0.5?1. Use budget constraints to express consumption levels, ct and ct+1. (Hint: Use income conditions given above in the budget constraint. Notice that there are two possible states in the second period.)2. Rewrite the utility maximization problem as choosing the optimal at alone. (Hint: Replace ct and ct+1 in the utility function with your answers from point 1. Use probabilities to derive the expected value in the utility function. Remember that a random variable that takes values x1 in state one with probability p and x2 in state two with probability 1 − p has the expected value E [x] = p.x1 + (1 − p).x2)3. Derive the first order condition and find the optimal value of savings, at. (Hint: The only control (choice) variable is at)4. Does household accumulate precautionary savings to self-insure against the scenario of low income in the second period? Why or why not?
- how then can we find the total utility given q1=24, q2=30 and q3=15When utility function U(q1, q2)=min{ 34.6 q1, 17 q2} and q1= 33 and q2= 60 are given, find utility level consumer gains?Show that a decision maker who has a linear utilityfunction will rank two lotteries according to their expectedvalue.