An office complex leases space to various companies. these leases include energy costs associated with heating during the winter. to anticipate costs in the coming year, the managers developed two random variables x and y to describe costs for equivalent amounts of heating oil (x) and natural gas (y) in the coming year. both x and y are measured in dollars per btu of heat produced. the complex uses both fuels for heating, with yσx=σy.
(a) if managers believe that costs for both fuels tend to rise and fall together, then they should model x and y as independent.
(b) because the means and sds of these random variables are the same, the random variables x and y are identically distributed.
(c) if told that the costs of heating oil and natural gas are uncorrelated, an analyst should then treat the joint distribution as p(x, y)=p(x)p(y).

In mexico, many garment or sewing shops found they could entice many young people to work for them if they offered clean, air conditioned work areas with high-quality locker rooms to clean up in after the work day. typically, traditional garment shops had to offer to get workers to apply for the hard, repetitive, and somewhat dangerous work. a. benchmark competitive wages b.compensating differentials c. monopoly wages d. wages based on human capital development of each employee

Lindor inc.'s $100 par value preferred stock pays a dividend fixed at 8% of par. to earn 12% on an investment in this stock, you need to purchase the shares at a per share price of

2. taxes paid for a given income level rosa is getting ready to do her taxes. she is single and lives in denver. rosa earned $60,000 in taxable income in 2015. she reviews the following table, which shows the irs tax rates for a single taxpayer in 2015. on annual taxable the tax rate (percent) up to $9,225 10.0 from $9,225 to $37,450 15.0 from $37,450 to $90,750 25.0 from $90,750 to $189,300 28.0 from $189,300 to $411,500 33.0 from $411,500 to $413,200 35.0 over $413,200 39.6 based on the irs table, rosa calculates that her marginal tax rate is when her annual taxable income is $60,000. rosa calculates that she owes in income taxes for 2015. rosa then calculates that her average tax rate is , based on the annual income level and the amount of taxes she owes for 2015. after figuring out what she owes in taxes in 2015, rosa decides to ask an accountant for tax advice. the accountant claims that he has found a legal way to shelter $4,000 of taxable income from the federal government. the maximum amount that rosa is willing to pay to learn this strategy and reduce her taxable income by $4,000 is . (hint: sheltering some income means finding a legal way to avoid being charged income tax on that income. for example, someone who has $50,000 in taxable income and shelters $10,000 pays income tax on only $40,000.)