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At equilibrium, the demand for coconuts will equal the supply of coconuts and the demand for labour will equal the supply of labour. Graphically this occurs when the diagrams under consumer and producer are superimposed. As a result, Crusoe ends up consuming at the same point he would have if he made all the above decisions together. In other words, using the market system has the same outcome as choosing the individual utility maximisation and cost minimisation plans. This means that a competitive equilibrium can exist. The merit of a competitive equilibrium is that an efficient allocation of resources is achievable.
Let's assume that there is another commodity that Crusoe can produce apart from coconuts, for example, fish. Now, Robinson has to decide how much time to spare for both activities, i. The boundary of the production possibilities set is known as the production-possibility frontier PPF. In this case, the resources and technological constraints are Robinson Crusoe's labour.
It is crucial to note that the shape of the PPF depends on the nature of the technology in use. In figure 6, the underlying assumption is the usual decreasing returns to scale, due to which the PPF is concave to the origin. In case we assumed increasing returns to scale, say if Crusoe embarked upon a mass production movement and hence faced decreasing costs, the PPF would be convex to the origin.
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The PPF is linear with a downward slope in two circumstances:. Suppose that Crusoe can produce 4 pounds of fish or 8 pounds of coconuts per hour. If he devotes L f hours to fish gathering and L c hours to gathering coconuts, he will produce 4L f pounds of fish and 8L c pounds of coconuts. Suppose that he decides to work for 12 hours a day. Then the production possibilities set will consist of all combinations of fish, F , and coconuts, C , such that.
This equation represents Crusoe's PPF. If Crusoe works one hour less on hunting fish, he will have 4 less fish. If he devotes this extra hour to collecting coconuts, he will have 8 extra coconuts. The MRT is thus,.
Under this section, the possibility of trade is introduced by adding another person to the economy. Suppose that the new worker who is added to the Robinson Crusoe economy has different skills in gathering coconuts and hunting fish. Friday can produce 8 pounds of fish or 4 pounds of coconuts per hour. If he too decides to work for 12 hours, his production possibilities set will be determined by the following relations:. This means that for every pound of coconuts Friday gives up, he can produce 2 more pounds of fish. So, we can say that Friday has a comparative advantage  in hunting fish while Crusoe has a comparative advantage in gathering coconuts.
Their respective PPFs can be shown in the following diagram:. The joint production possibilities set at the extreme right shows the total amount of both commodities that can be produced by Crusoe and Friday together. It combines the best of both workers. If we want more fish, we should shift that person who has a comparative advantage in fish hunting i. Friday out of coconut gathering and into fish hunting.
When Friday is producing 96 pounds of fish, he is fully occupied.
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If fish production is to be increased beyond this point, Crusoe will have to start hunting fish. If we want to produce only fish, then the economy will have pounds of fish, 48 from Crusoe and 96 from Friday. Thus the joint PPF is kinked because Crusoe and Friday have comparative advantages in different commodities. As the economy gets more and more ways of producing output and different comparative advantages, the PPF becomes concave. Assume that there are c units of coconut and f units of fish available for consumption in the Crusoe Friday economy.
Given this endowment bundle c , f , the Pareto efficient bundle can be determined at the mutual tangency of Crusoe's and Friday's indifference curves in the Edgeworth box along the Pareto Set contract curve. These are the bundles at which Crusoe's and Friday's marginal rate of substitution are equal. From the figure 8, it is clear that an economy operating at a position where the MRS of either Crusoe or Friday is not equal to the MRT between coconuts and fish cannot be Pareto efficient. This is because the rate at which, say Friday is willing to trade coconuts for fish is different from the rate at which coconuts can be transformed into fish.
For example, suppose we want to investigate the effect of a higher resource intrinsic growth rate r.
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To view the dynamic path to steady state equilibrium associated with the case shown in Figure 3, select an initial resource stock S 0 and human population L 0. Users may change these initial values by simply typing new values in the corresponding text boxes. An animated dynamic path cycles toward the steady state equilibrium intersection of the two isoclines.
To view the Time Paths of the resource stock S and population L for this version of the model, check the Time Paths checkbox and click the Path button again. Figure 5 shows the Time Paths of resource stock and population from A. It is clear from Figures 5 and 7 that a higher resource intrinsic growth rate supports a more robust population that recovers after A. The parameter sliders allow changes within the following ranges:.
Minimum Value. Maximum Value. Critical Depensation.
The Easter Island Modeling Software allows users to specify a critically depensated resource growth function with a minimum viable population of the type:. Figures 9 and 10 show the Phase Diagram and Time Paths views of the model in the presence of critically depensated growth. Note that the resource crashes in this model variant as the population L increases dramatically followed by a precipitous collapse that is reinforced when the resource stock drops below its minimum viable population. Figure 9: Phase Diagram view of the model. Figure Time Paths view of the model.
Incorporating Institutions. Dalton and Coats ask if institutional arrangements could have saved the Easter Island civilization from collapse. Dalton and Coats incorporate the institutional response parameter in the harvest employment equation as follows:. The EIMS software includes an Institutional Parameter slider that allows users to specify and fine tune the strength of institutions.
Consistent with Dalton and Coats model, three types of institutions are possible:. Type of Institutions. The route the train takes to the destination is up to the intelligent train. In theory, this sounds good - local knowledge and individual initiative are usually superior to central planning.
However, the personalities of the intelligent trains on Sodor are, for the most part, very naive and child-like. This is almost certainly a deliberate decision to prevent the trains from rising up and rebelling against their human masters. But as a consequence, the trains often find themselves losing cargo or delivering it late.
If you're going to have child-like trains, they're going to need guidance and direction. Their routes and schedules should be planned rather than relying on the unreliable trains to do their work. The Island of Sodor is pretty economically self-sufficient. It has farms, coal mines, quarries, zoos, and many other industries. And while that warms the heart of my inner 19th-Century Whig, in an era of globalization, it's not the Island's best economic decision.clublavoute.ca/jopam-paginas-para.php
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As David Ricardo described way back in the 18th century, economies should focus on their comparative advantages. AI research on the Island of Sodor is massively ahead of the rest of the world.
The trains on Sodor have been designed to understand natural language, solve problems for themselves, recognize new situations, and even have emotions and personalities. This is way, way ahead of artificial intelligence research in the rest of the world. Google , BMW, and many other car companies, for example, are working on driverless cars - a problem that Sodor has solved. Apple and Google are also working on natural language comprehension for use in voice-activiated search engines for phones.