Suppose that consumer is always ready to trade 3 units of X and 4 units of Y. Then, what would be the demand function for X? Px , then X Px If Py 4 then X = 0 and if PY Px I Px If PY 3. then X = 0 and if Py Px 3 then X 4 Px Px and if Py If Px then X then X = 0 Px
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- Suppose Var(X) = 36, Var(Y) = 42, and X and Y are independent. What is Var(.25X + .75Y)? Suppose Var(X) = 63, Var(Y) = 87, and X and Y are independent. What is Var(.79X + .21Y)? Suppose that Var(X) = 907.96, Var(X) = 10219.44, and Cov(X,Y) = 2694.59. What is Var(.33X + .67Y)?Suppose that the buyers do not know the quality of any particular bicycle for sale, but the sellers do knowthe quality of the bike they sell. The price at which a bike is traded is determined by demand and supply.Each buyer wants at most one bicycle.(ii) Assuming that each buyer purchases a bike only if its expected quality is higher than the price,and each seller is willing to sell their bike only if the price exceeds their valuation, what is theequilibrium outcome in this market?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…
- Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)Maximize Q=K^0.4L0.5 given the equation S+3K+4L=108At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees is choosing how many dollars to contribute from the interval [0,20]. The manager of these 20 employees announces that she will contribute dd dollars for every dollar that an employee contributes. The payoff to employee ii who makes contribution of xixi dollars is bi(1+d)xi−xi, where bi>0.bi(1+d)xi−xi, where bi>0. Assume that d=4d=4, bi=0.25bi=0.25 for i=1,2,…,10i=1,2,…,10, andbi=0.5bi=0.5 for i=11,12,…,20i=11,12,…,20 What is the best contribution level of any employee ii for i=1,2,…,10i=1,2,…,10. At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees is choosing how many dollars to contribute from the interval [0,20]. The manager of these 20 employees announces that she will contribute dd dollars for every dollar that an employee contributes. The payoff to employee ii who makes contribution of xixi dollars is bi(1+d)xi−xi,…
- An amount of money is accumulating; in period t (= 1, 2, . . . , T) its size is $2t. In each period two people simultaneously decide whether to claim the money. If only one person does so, she gets all the money; if both people do so, they split the money equally; and if neither person does so, both people have the opportunity to do so in the next period. If neither person claims the money in period T, each person obtains $T. Each person cares only about the amount of money she obtains. Formulate this situation as an extensive game with perfect information and simultaneous moves, and find its subgame perfect equilibria). (Start by considering the cases T = 1 and T = 2.)Suppose that you have a lottery with two states Yes and No. You are asked to toss a coin andthat if it comes up head, you will win 5% of your investment and if it comes up tail you willlose 3% of your investment. Assume that your initial investment is K1000 and that you havedecided to only toss a coin three times.i. Determine all the possible outcomes of the game at the end of the third toss andpresent your answer on a tree diagram. ii. What is the total wealth for each of the outcomes in (i) above? iii. Find the expected value of the outcomes.Given Q1 = 150 -3P1 + P2 + P3 Q2 = 180 +P1 - 4P2 + 2P3 Q3 = 200 +2P1 + P2 - 5P3 and TC =Q12 + Q1Q2 +2Q22 + Q2Q3 +Q32 + Q1Q3 Find the inversedemand function P = f(Q) and use Cramer’s rule to solve for thecritical value Q1. (Answer in two decimal places.) Use Cramer’s rule tosolve for the critical value Q2. (Answer in two decimalplaces.) Use Cramer’s rule tosolve for the critical value Q3. (Answer in two decimalplaces.) Calculate the Hessian matrix. What is the value of|H3|? (Answer in two decimal places.) Based on the Hessian, what can you say about the profit? (Answer in one word. )
- Assume that there are two parties, I and V. I engages in an activity that tends to injure V. V and I both can take care to reduce the expected harm from accidents. Specifically, suppose that if I takes no care (i.e., spends $0 on accident precautions), expected injury to V is $250. If I spends $40 on accident precautions, however, the expected injury to V is reduced to $175. Further suppose that V has a choice between taking no care or spending $50 in care to avoid accidents. If V spends $50 in care, V’s expected harm falls by $20 regardless of the level of care that I takes. Assume that courts adopt the socially‐optimal level of injurer care as the negligence standard. That is, if I takes less than the socially‐optimal level of care, she will be found negligent and must pay for all damages to V. If I takes at least the socially optimal level of care, she will not have to compensate V for his damages. 1. Under a negligence standard, what is I’s dominant strategy? a) I does not have a…Suppose the production functions of the decision maker belowindicate the effect of seeding rate on yield in the two states:y1 = −1.6 + 0.085x − 0.0005x2 wet season y2 = −1.7 + 0.087x − 0.0006x2 dry season with yi the yield per hectare in tonnes according to state i;where x is the seed rate in kilograms per hectare.For a wet year i = 1 and a dry year i = 2.These functions are shown in the following figure. Suppose the price of wheat is pw = 150$/t, the price of seedspx = 0.15$/kg and that the other variable costs are v = 110$/ha on a sown area of a = 50ha. Calculate the net income of this farmer in the above case.What is the optimal decision for the farmer in this case?Let P(A) = 0.2, P(B) = 0.6 and P(A or B) = 0.5. Are events A and B mutually exclusive? Why or why not?
