Xenos and Yvonne are marooned on an island. Each castaway cares only about their own consumption. They are surviving by fishing and gathering plants to eat. Both have diminishing marginal rates of substitution of fish for plants. However, due to differing abilities, Yvonne catches most of the fish and Xenos gathers most of the plants. In each period, the results of their own work constitute their initial endowment.
1. Draw an Edgeworth box showing the two castaways’ exchange economy for fish and plants. The dimensions of the box represent the fish and gathered plants that they assemble in a single period. Mark an appropriate endowment point before trade, given their relative abilities in fishing and gathering stated above.
2. The castaways then trade fish for plants. Sketch onto your box two or three indifference curves for each castaway, and a contract curve. Identify points on the contract curve that could be reached via trade where both Xenos and Yvonne would be better off. Explain your answer.
3. Sketch a budget constraint and, if necessary, additional indifference curves to identify an exchange optimum after trade. Explain your answer.
4. What can you say about the efficiency of this outcome? Explain your answer in full.
5. Assume Yvonne’s preferences change such that she becomes more caring. Explain, using a diagram, how these new preferences might affect the contract curve and the equilibrium point in their exchange economy.
1. Xenos and Yvonne are marooned in an island. They are surviving by fishing and gathering plants and both of them have diminishing marginal rates of substitution of fish for plants. But Yvonne catches most of the fish and Xenos gathers most of the plants (Bernheim and Rangel, 2005). In the following diagram, the Edgeworth box diagram can be drawn for showing the exchange economy for fish and plants.
In the above diagram, the economy for fish and plants are shown between the two survivors. Ox is the origin of consumption of Xenos and Oy is the origin of consumption for Yvonne (Simonetti et al., 2010). In the above diagram the endowment point for both the survivors are given as A. It is known that Yvonne collects most of the fish and Xenos collects most of the plants. So, before trade their endowment point will be at A (Bernheim and Rangel, 2005).
2. Now, the castaway trades fish for plants. So, in the following diagram, the indifference curves can be drawn for each castaway along with the contract curve (Helm, 1989).
In the above diagram the two origins of both the survivors are shown. The quantities of Fish are measured horizontally and the quantities of plants are measured vertically. The total height of the box measures the total plants in the economy whereas the width of the box measures the total fish in the economy. X1, X2 and X3 represents Xenos’s indifference curves whereas Y1, Y2 and Y3 represent Yvonne’s indifference curves. A higher indifference curve represents higher level of utility (Kay, 2003). OxOy is the contract curve that is the locus of all tangent points of the indifference curves of both the survivors. B is an optimal point than A. If the consumption moves from point A to point B then both Xenos and Yvonne will move to higher indifference curve and thus both of them will be better off (Persky, 1989).
3. Now a budget constraint can be drawn between both the survivors.
In the above diagram the budget line is shown for the survivors. AD is the budget line that passes through the initial endowment point. In the above diagram, it can be seen that for Xenos, the initial endowment of plants was Op1 and the initial endowment of fish was Of1. Xenos can trade plants for fish (Wilkinson, 1996). Thus, after trade between both the survivors, Xenos can move to point B where he consumes Of2 units of fish and Op2 amount of plants. Similarly from Yvonne’s point of view he trades fish for plants and point B is the optimal point for both the survivors in the island.
4. Here it can be said that the outcome is efficient for both the survivors. It is known that fish and plants are both required for a healthy diet in the island. It is known that the marginal rates of substitution are diminishing of fish for plants. That means, lower amount of fish will be given up by Yvonne for gaining more plants. On the other hand, the welfare of both the person should be taken into consideration. It is known that higher indifference curve means higher welfare of a person and thus it is very important to achieve the highest possible indifference curve for the individuals (Wilkinson and Pickett, 2009). So, it is very important to achieve the pareto optimal point. It is evident that if they move from the pareto optimal point then no one can be made better off without making anyone worse off. Thus it can be said that the outcome is efficient as the point is a pareto optimal point.
5. If Yvonne’s preference changes and she becomes more caring then she will consider not only her preference but she will also take into account the preference of Xenos. Now, in the following diagram the change in the contract curve can be shown.
If the preference changes to more altruistic nature then the optimal point for Yvonne will be at B and similarly the optimal point for Xenos will be C. Thus the section of the contract curve from Ox to B will not be effective and similarly the section Oy to point C will not be effective. In this case the section B to C of the contract curve will now be pareto efficient for both the survivors (Wilkinson and Pickett, 2009).
Bernheim, B. and Rangel, A. (2005). Behavioral public economics. Cambridge, MA: National Bureau of Economic Research.
Helm, D. (1989). The Economic borders of the state. Oxford: Oxford University Press.
Kay, J. (2003). The truth about markets. London: Allen Lane.
Persky, J. (1989). Retrospectives: Adam Smith's Invisible Hands. Journal of Economic Perspectives, 3(4), pp.195-201.
Simonetti, R., Himmelweit, S., Mackintosh, M. and Stone, H. (2010). Doing economics : people, markets and policy. Book 1. Milton Keynes : Open University
Wilkinson, R. (1996). Unhealthy societies. London: Routledge.
Wilkinson, R. and Pickett, K. (2009). The spirit level. London: Allen Lane.
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