Macroeconomics 1

Write down a single term expression to represent the present value of a deferred

annuity-due of 1 pa payable to a life now aged x , with a deferment period of n years.

Hence derive a formula for the variance of the present value of this contract (hard!)

Q1The model of Demand and Supply works best when applied to competitive markets.

The assumptions of competitive markets include a large number of sellers, each small in comparison to the size of the market. Consistent with this is the added assumption that entry into a competitive market is not prohibitively expensive or difficult. Another assumption that is more problematic is that all of the sellers are providing identical, or nearly identical, products. This does not seem like a realistic assumption, as not at least trying to distinguish one's own product from the rest goes against the spirit of competition and modern-day marketing!

Nevertheless, examples of competitive markets do seem to be found at least in a few markets, such as those for agricultural products. The reason is that the processing, packaging, and branding that often help to distinguish products is minimal. For example, "corn" as a raw agricultural product is seen as relatively undifferentiated from the competition, whereas bags of frozen, ready to cook corn, with a well-recognized brand name clearly displayed, are possibly quite differentiated to the average consumer.

For this Discussion, find an example of a change or disruption in the market for some agricultural products. An easy place to begin looking could be weather-related news or analysis of food trends.

Describe what is happening in the market and why. Be precise.

Do you think that because of the disruption the Demand curve is shifting, the Supply curve is shifting, or both?

What is the direction of the shift in the curve?

What do you expect would be the effect on the equilibrium price and quantity in this market

What do you think might happen in the future, over the long run?

Cite any articles or outside information used in APA format.

Suppose that PrArt is decreasing for 0 0, s(x) = (1 -x/w)" (05xsu) Give simple formulae for (i) (ii) er (Note finite limiting age), (iii) 10P70; (iv) 40 5935 A certain group of lives now aged 60 experience mortality according to a(55) males ultimate with addition to the force of mortality. The addition is 0.0005 at age 60, increasing linearly to 0.0025 at age 80, at which level the addition remains constant. Find the probability that a life aged exactly 60 dies within 20 years