Samantha, who is single and has MAGI of $58,500, was recently employed by an accounting firm. During the year, she spends $3,900 for a CPA exam review course and begins working on a law degree in night school. Her law school expenses were $5,040 for tuition and $780 for books (which are not a requirement for enrollment in the course).

Lillypad toys is a manufacturer of educational toys for children. six months ago, the company's research and development division came up with an idea for a unique touchscreen device that can be used to introduce children to a number of foreign languages. three months ago, the company produced a working prototype, and last month the company successfully launched its new device on the commercial market. what should lillypad's managers prepare for next? a. increased competition from imitators b. a prolonged period of uncontested success c. a sharp decline in demand for the product d. a difficult struggle to move from invention to innovation

A$100 million interest rate swap has a remaining life of 10 months. under the terms of the swap, the six-month libor is exchanged semi-annually for 12% per annum. the six-month libor rate in swaps of all maturities is currently 10% per annum with continuous compounding. the six-month libor rate was 9.6% per annum two months ago. what is the current value of the swap to the party paying floating? what is its value to the party paying fixed?

David consumes two things: gasoline (g) and bread (b). david's utility function is u(g, b) = 10g^0.25 b^0.75. use the lagrange technique to solve for david's optimal choices of gasoline and bread as a function of the price of gasoline, p_g, the price of bread, p_b, and his income m. with recent decrease in the price of gasoline (maybe due to external shock such as shale gas production) does david increase his consumption of gasoline? for david, how does partial differential g/partial differential p_g depend on his income m? that is, how does david's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? to answer these questions, find the cross-partial derivative, |partial differential^2 g/partial differential m partial differential p_g.