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I do not understand how the graph was derived, where is the graph showing the perfect complements, step by step explanations into all parts, thanks

image text in transcribedimage text in transcribed

I do not understand how the graph was derived, where is the graph showing the perfect complements, step by step explanations into all parts, thanks

image text in transcribedimage text in transcribed
* Bert and Ernie are atmates. They both eat cream cheese and chocolate spread for breakfast Bert has an initial endowment consisting of 10 units of cream cheese and 10 units of chocolate spread. Ernie's initial endowment consists of 10 units of cream cheese and 20 units of chocolate spread. Bert regards both products as perfect 1-for-1 substitutes. Ernie regards them as perfect complements, and always mixes 3 units of chocolate spread with 2 units of cream cheese for his perfect croissant filling. a. Represent these initial endowments in an Edgeworth exchange box. b. Describe the set of allocations that are Pareto preferred to the initial endowment. c. Describe the contract curve for that allocation. d. What price ratio will be required to sustain an allocation on the contract curve? e. How will your answers to the above questions differ if 5 units of Ernie's chocolate spread endowment are given to Bert? Ernie's chocolate spread 30 20 15 10 Of 20 Contract Curve Bert's cream cheese 10 10 Ernie's cream cheese initial Pareto- allocation Superior Set 20 OB 10 15 20 30 Berth's chocolate spread b. Because Bert regards cream cheese and chocolate spread as perfect substitutes his indifference curve is a 45 degree downward sloping line. Because Ernie considers them as complements his indifference curve is L shaped. Moreover, 10 units of cream cheese and 20 units of chocolate spread gives the same utility as 10 units of cream cheese and 15 units of chocolate spread. The Pareto-superior set contains all the points that would allow both Bert and Ernie both move to higher indifference curves at the same time. It is represented by the shaded triangle in the diagram. c. The contract curve consists of all Pareto efficient points. Those are the points for which the Pareto-superior set is empty - Bert's indifference curves go through the corner point of Ernie's indifference curves. Neither of the two can achieve higher utility without making the other less happy. Because of the shape of Ernie's indifference curves, at any Pareto efficient point Ernie has 3 units of chocolate spread for every 2 units of cream cheese. The contract curve is a straight line in this case (blue line in the diagram). d. The only price ratio that sustains an allocation on the contract curve is 1. Suppose the price ratio is not equal to 1. Then, since Bert sees the products as perfect substitutes, he will always want to consume only the cheapest one. Thus, the allocation on the contract curve is not sustained, Bert will either consume only cream cheese or only chocolate spread. On the other hand, when the prices are equal to each other he is indifferent between all possible combinations of the cheese and the spread in his breakfast. And thus, an allocation on the contract curve is sustained

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