Your grandparents have an annuity. the value of the annuity increases each month by an automatic deposit of 1% interest on the previous month's balance. your grandparents withdraw $1000 at the beginning of each month for living expenses. currently, they have $50,000 in the annuity. model the annuity with a dynamical system. will the annuity run out of money? when? hint: what value will an have when the annuity is depleted?

Consider the market for gasoline. suppose that, in a competitive market without government regulations, the equilibrium price of gasoline is $3.00 per gallon, and employees at gas stations earn $17.50 per hour. complete the following table by indicating whether each of the statements is an example of a price ceiling or a price floor and whether it results in a shortage or a surplus or has no effect on the price and quantity that prevail in the market. statement price control effect the government has instituted a legal minimum price of $3.40 per gallon for gasoline. the government prohibits gas stations from selling gasoline for more than $3.40 per gallon. due to new regulations, gas stations that would like to pay better wages in order to hire more workers are prohibited from paying more than $14.50 per hour.

Leticia has worked for 20 years in the public relations department of a large firm and has been the vice-president for the past ten years. it is unlikely she will ever be promoted to the top executive position in her firm even though she has directed several successful projects and is quite capable. her lack of promotion is an illustration of (a) the "glass ceiling" (b) the "glass elevator" (c) the "mommy track" (d) sexual harassment

In the united states, one worker can produce 10 tons of steel per day or 20 tons of chemicals per day. in the united kingdom, one worker can produce 5 tons of steel per day or 15 tons of chemicals per day. the united kingdom has a comparative advantage in the production of: