Catherine is using the table to predict the cost of one year of education at a four-year private college. category predicted cost tuition $32,250 room and board $10,590 transportation $2,460 books and fees $1,980 other $750 she predicts she will receive $14,000 in grants annually. catherine does not own a car and plans to live near campus where she will rely on the free bus system for transportation. what is the minimum amount catherine should expect to contribute to her education annually?

Define the marginal rate of substitution between two goods (x and y). if a consumer’s preferences are given by u(x, y) = x3/4y1/4, compute the consumer’s marginal rate of substitution as a function of x and y. calculate the mrs if the consumer has chosen to consumer 48 units of x and 16 units of y. show your work. (use the back of the page if necessary.

Fanning company is considering the addition of a new product to its cosmetics line. the company has three distinctly different options: a skin cream, a bath oil, or a hair coloring gel. relevant information and budgeted annual income statements for each of the products follow. skin cream bath oil color gel budgeted sales in units (a) 110,000 190,000 70,000 expected sales price (b) $8 $4 $11 variable costs per unit (c) $2 $2 $7 income statements sales revenue (a × b) $880,000 $760,000 $770,000 variable costs (a × c) (220,000) (380,000) (490,000) contribution margin 660,000 380,000 280,000 fixed costs (432,000) (240,000) (76,000) net income $228,000 $140,000 $204,000 required: (a) determine the margin of safety as a percentage for each product. (b) prepare revised income statements for each product, assuming a 20 percent increase in the budgeted sales volume. (c) for each product, determine the percentage change in net income that results from the 20 percent increase in sales. (d) assuming that management is pessimistic and risk averse, which product should the company add to its cosmetics line? (e) assuming that management is optimistic and risk aggressive, which product should the company add to its cosmetics line?

You own 2,200 shares of deltona hardware. the company has stated that it plans on issuing a dividend of $0.42 a share at the end of this year and then issuing a final liquidating dividend of $2.90 a share at the end of next year. your required rate of return on this security is 16 percent. ignoring taxes, what is the value of one share of this stock to you today?