Econ 280 Midterm Student Number: ______
1. The market price of a unit of housing measures what? (4 out of 30 marks)
The market price of a unit of housing measures the value-in-trade of the next unit of housing to participants in a particular market at a particular time. It is determined by supply, which reflects marginal cost, and demand, which reflects marginal willingness and ability to pay.
2. Using a graph with the standard-of-living on the horizontal axis, and rates of change on the vertical axis, draw a Malthusian depiction of equilibrium. Show birth rates rising at every standard of living. Where is the new equilibrium? Why? (3 marks)
The new equilibrium (B) occurs at a higher standard of living than before. At this new standard of living, there are fewer births per thousand per year, and fewer deaths per thousand per year. Formerly, this standard of living would have caused the birth rate to exceed the death rate, leading to population growth; this population growth would have driven the standard of living back down to A. However, now that birth rates have fallen, the standard of living at B is compatible with zero population growth.
3. Consider a human population that is living under Malthusian conditions. Think about mortality rates and sex ratios which might be typical for each age group. Then make up some population size numbers for the following table. After that, describe three features of the numbers you have entered which makes them plausible for the "Age of Pestilence and Famine".
(4 marks)
Year1690 / newborns / 1-9 / 10-19 / 20-29 / 30-39 / 40-49 / 50+ / All Ages
Male
Female
The numbers here should indicate:
1) Mortality is generally high. There are fewer people at older ages.
2) Infant mortality is particularly high. There is a big drop-off in numbers at age 1-9.
3) The sex ratio rises during ages 10-29 because of deaths in childbirth.
4. If a population of 40,000 people grew to be 60,000 in 10 years, at what rate did it grow, assuming exponential growth? Show your work. (2 marks)
60,000=40,000 exp(10r)
1.5 = exp(10r)
ln(1.5) = 10r
0.4055 = 10 r
r = 0.04055 or approximately 4%.
5. Given this population projection matrix, A = ,
and an age vector n(t)= , what will the age vector be next year? (i.e. what is n(t+1)?)
(2 marks)
n(t+1)= =
6. Write an expression for the value of a payment of $1,000 received each year for the first 8 years of your child's life. The first payment is received at birth. Value each payment relative to the value of money received at your child's birth date. Money can earn interest at rate 5%. Use either yearly (geometric) or continuous (exponential) compounding. (1 mark)
or
7. Complete the following Life Table. Write down any assumptions you feel you must make. If you can't get a cell which you need in order to continue, call the value in that cell "x" and proceed for part marks. Show your work for part marks. There is more space on the next page. (4 marks)
AgeRange / n / q / l / d / L / T / e<1 / 1.00 / 0.02 / 100,000 / 2000 / 98,200 / 852,800 / 8.5
1-4 / 4.00 / 0.05 / 98,000 / 4,900 / 382,200 / 754,600 / 7.7
5+ / unknown / 1.00 / 93,100 / 93,100 / 372,400 / 372,400 / 4
One mark was earned for the "L" entry, and one for the "T" entry in the last row. All other entries were worth 1/8 of a mark each.
8. If the population whose mortality is described by the Life Table above is stationary, what is the percentage of newborns in the population? (2 marks)
The fraction of newborns in the population = 100,000/ (100,000+98,000+93,100) = 0.34. Thus 34 percent of the population is newborn.
9. You have been hired to design a policy that will reduce deaths of elderly people resulting from falls. Focus on an important cause of deaths from falls, identify your target group precisely, and discuss how your policy addresses constraints and margins. Who bears most of the cost of your policy? (8 marks)
Sample answer: Many elderly people die from falls because they lie on the ground for hours or days without anyone being aware that they have fallen. In this case we need to reduce the isolation which prevents them from being found and treated promptly. This is the constraint we are working to ease. Our target group is the elderly who live alone, especially the frail elderly. One idea is to encourage them towear emergency 911 call transmitters around the neck or wrist. These elders are likely to watch a fair bit of TV, and advertising on popular daytime channels might be effective. Doctors and pharmacists can also be encouraged to promote the product. The taxpayers pick up the tab for the advertising. Demand for the transmitters will rise, and the price of the transmitter and transmission services is likely to rise. The more elastic the supply, and the greater the ease of entry into the industry, the less the price rise will be. People who already have transmitters will be hurt if their service charges increase.
In the case of elderly falls, we want to prevent time delay after any and all falls. The emergency call transmitter does that if it is worn every day.