Oxford economics and management test 2002
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THE COLLEGES OF OXFORD UNIVERSITY
ECONOMICS AND MANAGEMENT
THURSDAY, 12 DECEMBER 2002 11 a.m.
Time allowed: 15 minutes for reading through the questions and 1 hour when you may write.
For candidates applying for the joint school of Economics and Management
Answer questions 1 and 2 in Section A, and as many questions as you can in Section B. Each question carries equal marks.
SECTION A
Read the following passage carefully and answer both questions.
'Too Many Mouths': The Economics of Rev. Malthus
In the United States of America, where the means of subsistence have been more ample, the manners of the people more pure, and consequently the checks to early marriages fewer, than in any of the modem states of Europe, the population has been found to double itself in twenty-five years.
This ratio of increase, though short of the utmost power of population, yet as the result of actual experience, we will take as our rule, and say, that population, when unchecked, goes on doubling itself every twenty-five years or increases in a geometrical ratio.
Let us now take any spot of earth, this Island for instance, and see in what ratio the subsistence it affords can be supposed to increase. We will begin with it under its present state of cultivation. If I allow that by the best possible policy, by breaking up more land and by great encouragements to agriculture, the produce of this Island may be doubled in the first twenty-five years, I think it will be allowing as much as any person can well demand.
In the next twenty-five years, it is impossible to suppose that produce could
be quadrupled. It would be contrary to all our knowledge of the qualities
of land. The
very utmost that we can conceive, is, that the increase in the second twenty-five
years might equal the present produce. Let us then take this for our rule,
though certainly far beyond the truth, and allow iIiar,15y great exertion,
the whole produce of the Island might be increased every twenty-five years,
by a quantity of subsistence equal to what it at present produces. The most
enthusiastic speculator cannot suppose a greater increase than this. In a
few centuries it would make every acre of land in the Island like a garden.
Yet this ratio of increase is evidently arithmetical.
It may be fairly said, therefore, that the means of subsistence increase in an arithmetical ratio. Let us now bring the effects of these two ratios together.
The population of the Island is computed to be about seven millions, and we will suppose the present produce equal to the support of such a number:-In the first twenty-five years the population would be fourteen millions, and the food being also doubled, the means of subsistence would be equal to this increase. In the next twenty-five years the population would be twenty-eight millions, and the means of subsistence only equal to the support of twenty-one millions. In the next period, the population would be fifty-six millions, and the means of subsistence just sufficient for half that number. And at the conclusion of the first century the population would be one hundred and twelve millions and the means of subsistence only equal to the support of thirty-five millions, which would leave a population of seventy-seven millions totally unprovided for.
No limits whatever are placed to the productions of the earth; they may increase for ever and be greater than any assignable quantity. Yet still the power of population being a power of a superior order, the increase of the human species can only be kept commensurate to the increase of the means of subsistence by the constant operation of the strong law of necessity acting as a check upon the greater power.
The effects of this check remain now to be considered.
We will suppose the means of subsistence in any country just equal to the easy support of its inhabitants. The constant effort towards population, which is found to act even in the most vicious societies, increasing the number of people before the means of subsistence are increased. The food therefore which before supported seven millions must now be divided among seven millions and a half or eight millions. The poor consequently must live much worse, and many of them be reduced to severe distress. The number of labourers also being above the proportion of the work in the market, the price of labour must tend toward a decrease, while the price of provisions would at the same time tend to rise. The labourer therefore must work harder to earn the same as he did before. During this season of distress, the discouragements to marriage, and the difficulty of rearing a family are so great that population is at a stand. In the mean time the cheapness of labour, the. plenty of labourers, and the necessity of an increased industry amongst them, encourage cultivators to employ more labour upon their land, to turn up fresh soil, and to manure and improve more completely what is already in tillage, till ultimately the means of subsistence become in the same proportion to the population as at the period from which we set out. The situation of the labourer being then again tolerably comfortable, the restraints to population are in some degree loosened, and the same retrograde and progressive movements with respect to happiness are repeated.
This sort of oscillation will not be remarked by superficial observers, and it may be difficult even for the most penetrating mind to calculate its periods. Yet that in all old states some such vibration does exist, though from various transverse causes, in a much less marked, and in a much more irregular manner than I have described it, no reflecting man who considers the subject deeply can well doubt.
Taken drom T. Malthus, An Essay on the Principle of Population, 1798. (The
Island is Great Britain.)
1. Summarize the passage in your own words, using no more than 100 words.
2. Are Malthus' warnings about the effects of population growth relevant in the twenty-first century?
SECTION B
3. Farmer A and Farmer B both keep sheep and obtain wool from them. Farmer A's profit when she has SA sheep producing wool is vSA. She has a flock of sixteen sheep initially. Her sheep are vulnerable to a disease. The probability that A's flock catches the disease is 0.5. Whenever the disease is present in the flock twelve sheep catch the disease. Diseased sheep produce no wool and hence no profit. The remaining four sheep, however, are unaffected and continue to produce wool. Farmer B operates in a different region to A and the disease is not present in this area. His profit when he has SB sheep is simply SB. B has ten sheep, so his profit is 10. You can assume that all farmers aim to obtain the highest possible expected profit.
(a) What is farmer A's expected profit?
Farmer B proposes the following contract to A. If the disease affects A's
flock then B
will give 5 sheep to A. lithe disease does not affect A's flock then A gives
B 7 sheep.
(b) What is farmer A's expected profit when she makes this contract with
B?
( c) What is farmer B' s expected profit when this contract is made with A?
(d) Who benefits from the contract?
Another farmer, C, has the same characteristics as B. C, however, proposes a contract with A of the following form. If the disease affects A's flock C will give A 6 sheep. If the disease does not affect A's flock A gives C 6 sheep. Call this the second contract.
(e) Which contract does A prefer, the first or the second? Give reasons for
your
answer.
(f) What is the expected profit of farmer C with the second contract?
(g) Who benefits from the second Contract? Comment on your answer.
(h) Is there a third type of contract which ensures that both parties to the
contract are better off than with no contract? If so, describe what it might
look like.
4. A football club is considering its pricing policy for season tickets for the coming season. The holder of a season ticket is guaranteed a seat in the stadium. The main cost of the club is the players' wages, and these have already been fixed at £3m. It also pays a rent of £I.5m for the use of its current stadium, which has a capacity of 50,000, but it has the option of moving to a new stadium seating 60,000 at a rent of £2m. It hires a business consultant who calculates that at last season's annual ticket price of £I 00 it will just fill its current stadium. If the price is increased by 10% then the current stadium will be at 80% capacity, so 40,000 tickets will be sold. If the price is cut by 10% then the number of fans wanting season tickets will increase by 20% to 60,000. The club wants to maximize its profits and has to decide (i) whether to move to the new stadium or to remain in the existing one and (ii) whether to keep the current price of £1 00, to raise it by 10% to £110 or to cut it by 10% to £90.
(a) What do you predict that the club will do? Explain your reasons.
(b) What would be the level of annual rent for the new stadium that would
imply that the club makes the same level of profit whether it moves or stays?
(You can assume that the club still has the option of changing the price.)
(c) The club now finds that a third option is available. The existing stadium
can be redesigned to seat 60,000, and the owner of the stadium will charge
an extra £300,000 in rent for this refurbished stadium. What will the
club do now?
(d) What now would be the highest level of the annual rent for the new stadium
that would encourage the club to move there?