Hansel and gretel, a married couple, manage apartments and they are required to live in the managers' apartment as a condition of their employment. instead of providing the apartment to hansel and gretel rent-free, the owner of the apartment building gives hansel and gretel a housing allowance of $600, which they use to pay rent on the managers' apartment. hansel and gretel pay $600 per month in rent. if they did not live in the managers' apartment, hansel and gretel could live in another apartment building where they would only pay $500 in rent. what amount, if any, must be included in hansel and gretel's gross income?

Four analysts cover the stock of fluorine chemical. one forecasts a 6% return for the coming year. the second expects the return to be negative 6%. the third predicts a return of 8%. the fourth expects a 2% return in the coming year. you are relatively confident that the return will be positive but not large, so you arbitrarily assign probabilities of being correct of 35 % comma 8 %, 17 %, and 40%, respectively, to the analysts' forecasts. given these probabilities, what is fluorine chemicals expected return for the coming year

Suppose that two firms produce differentiated products and compete in prices. as in class, the two firms are located at two ends of a line one mile apart. consumers are evenly distributed along the line. the firms have identical marginal cost, $60. firm b produces a product with value $110 to consumers.firm a (located at 0 on the unit line) produces a higher quality product with value $120 to consumers. the cost of travel are directly related to the distance a consumer travels to purchase a good. if a consumerhas to travel a mile to purchase a good, the incur a cost of $20. if they have to travel x fraction of a mile, they incur a cost of $20x. (a) write down the expressions for how much a consumer at location d would value the products sold by firms a and b, if they set prices p_{a} and p_{b} ? (b) based on your expressions in (a), how much will be demanded from each firm if prices p_{a} and p_{b} are set? (c) what are the nash equilibrium prices?

Bridge building company estimates that it will incur $1,200,000 in overhead costs for the year. additionally, the company estimates 50,000 direct labor hours will be spent building custom walking bridges for the year at a total direct labor cost of $600,000. what is the predetermined overhead rate for bridge building company if direct labor costs are to be used as an allocation base?