The manufacturer of a product (p) currently controls 20% of the market in a particular country, while the rival brand (q) controls the rest of the market. data from previous year show that 75% of p’s customers remained loyal, while 25% switched to the rival brand. in addition, 50% of the competition’s customers did not switch to p during the year while the other 50% did. (a) respresenting the market share of each brank as a vector (whose components are fractions), formulate the problem of determining the market share next year, given the market share this year, as a matrix-vector problem (b) use the eigenvalues and eigenvectors of the matrix in (a) or any other method to determine the market share of the two products in the long run

Arriving and delivering a load of company executives for a business meeting at a destination far from home base requiring an overnight stay, a company’s pilot requested approval from the company finance office to pay to either have the company’s jet brought into the fbo's hangar overnight to protect it from a forecast snowfall or to have it de-iced by the fbo the following morning well-before scheduled departure. the company was under considerable financial pressure at the time, and the pilot’s requests were denied because of the cost. so, early the following morning, the pilot was up on the wing of the jet sweeping off an accumulation of snow and ice with a borrowed push broom in preparation for the scheduled departure with the executives, but slipped and fell to the ground, suffering a broken neck. the business was organized as a limited partnership, owned by 3 limited partners and one general partner. as a cost-saving measure, the company had dropped its workers’ compensation insurance before the accident. analyze the potential liability for the pilot’s injuries of each of the following, showing your reasoning clearly: the company the general partner the limited partners analyze how the outcome would have been different, if the business had been organized as a corporation and observed all of the formalities to legitimize its corporate status. analyze how the outcome would have been different, if the pilot had been covered by workers’ compensation insurance.

Recently, verizon wireless ran a pricing trial in order to estimate the elasticity of demand for its services. the manager selected three states that were representative of its entire service area and increased prices by 5 percent to customers in those areas. one week later, the number of customers enrolled in verizon's cellular plans declined 4 percent in those states, while enrollments in states where prices were not increased remained flat. the manager used this information to estimate the own-price elasticity of demand and, based on her findings, immediately increased prices in all market areas by 5 percent in an attempt to boost the company's 2016 annual revenues. one year later, the manager was perplexed because verizon's 2016 annual revenues were 10 percent lower than those in 2015"the price increase apparently led to a reduction in the company's revenues. did the manager make an error? yes - the one-week measures show demand is inelastic, so a price increase will decrease revenues. yes - the one-week measures show demand is elastic, so a price increase will reduce revenues. yes - cell phone elasticity is likely much larger in the long-run than the short-run. no - the cell phone market must have changed between 2011 and 2012 for this price increase to lower revenues.

Explain whether each of the following events increases or decreases the money supply. a. the fed buys bonds in open-market operations. b. the fed reduces the reserve requirement. c. the fed increases the interest rate it pays on reserves. d. citibank repays a loan it had previously taken from the fed. e. after a rash of pickpocketing, people decide to hold less currency. f. fearful of bank runs, bankers decide to hold more excess reserves. g. the fomc increases its target for the federal funds rate.