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In: Economics

6. Consider a pure exchange economy with two individuals, Sarah and James, and two goods, X...

6. Consider a pure exchange economy with two individuals, Sarah and James, and two goods, X and Y . For Sarah, goods X and Y are perfect complements (Leontief preferences), so her utility function is US = min {XS, YS}. For James, goods X and Y are perfect substitutes, so his utility function is UJ = XJ + YJ . Suppose the economy has 100 units of good X and 50 of good Y . Draw indifference curves for Sarah and James in an Edgeworth box and sketch the contract curve. Explain your diagram.

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Expert Solution

6. In the pure exchange economy with two individuals, Sarah and James, and two goods, X and Y.

For Sarah, goods X and Y are perfect complements (Leontief preferences), so her utility function is

US = min {XS, YS}

Sarah's indifference curves are L shaped.

For James, goods X and Y are perfect substitutes, so his utility function is

UJ = XJ + YJ

James's indifference curves are negaticely sloped straight lines.

The economy has 100 units of good X and 50 units of good Y.

Now, the following diagram shows the indifference curves for Sarah and James.

Figure 1: Indifference curves of Sarah and James. AB is the contract curve.

Sarah's indifference curves are ICS1, ICS2 and ICS3. James's highest indifference curves corresponding to Sarah's indifference curves are ICJ1, ICJ2, ICJ3 respectively.

The pareto optimal points are along the line AB i.e. e1, e2 and e3. Hence the red line AB contains all the pareto optimal points.

​​​​​​The red line AB in the diagram is the contract curve.

Hope the diagram is clear to you my friend.

Rahul Sunny answered 1 year ago
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