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II. Assume Asmaa has Income = LE3200, that she spends buying rice X and vegetables Y. She faces the prices PX = LE100 per kilo and PY = LE70 per kilo. If U(X,Y) = 2x1/2 + 471/2, a) Set up Asmaas utility maximization problem. b) Solve for Asmaa's demand functions for commodities X and Y; and calculate their Marshallian demand at the above given prices. c) Is her solution interior or corner? And why? d) Is the consumer's marginal rate of substitution (MRS) increasing, decreasing or constant? What does that tell us about the shape of the indifference curves? Interpret your answer. e) Show graphically Asmaa's budget set with its axes' intersection. Find relative price of rice in terms of vegetables. Give economic interpretation of the relative price. Where can the relative price be seen in the graph of a budget set? f) The government wants to minimize the consumption of vegetables. It imposes a tax of LE10 per one kilo of vegetables if consumption exceeds 5 kilos of vegetables. Less than or equal to 5 kilos, the price of vegetables is the same at LE70. Plot graphically Asmaa's budget line without tax and with tax; and explain your answer with economic intuition. (Plot d and e on the same graph) g) What is the cross-price elasticity of demand of commodity X if price of Y increases by LE10, given the same income level and same price of X? Interpret your answer. h) Find the change in consumption of good Y due to its price decrease to LE50. Then, decompose the total effect into the substitution and income effects. Show your steps and interpret results analytically and graphically. (Hint: Show all changes on the same diagram. Indicate at what values they intersect the budget lines) i) Given the sign of the substitution and income effects, what is the type of commodity Y? II. Assume Asmaa has Income = LE3200, that she spends buying rice X and vegetables Y. She faces the prices PX = LE100 per kilo and PY = LE70 per kilo. If U(X,Y) = 2x1/2 + 471/2, a) Set up Asmaas utility maximization problem. b) Solve for Asmaa's demand functions for commodities X and Y; and calculate their Marshallian demand at the above given prices. c) Is her solution interior or corner? And why? d) Is the consumer's marginal rate of substitution (MRS) increasing, decreasing or constant? What does that tell us about the shape of the indifference curves? Interpret your answer. e) Show graphically Asmaa's budget set with its axes' intersection. Find relative price of rice in terms of vegetables. Give economic interpretation of the relative price. Where can the relative price be seen in the graph of a budget set? f) The government wants to minimize the consumption of vegetables. It imposes a tax of LE10 per one kilo of vegetables if consumption exceeds 5 kilos of vegetables. Less than or equal to 5 kilos, the price of vegetables is the same at LE70. Plot graphically Asmaa's budget line without tax and with tax; and explain your answer with economic intuition. (Plot d and e on the same graph) g) What is the cross-price elasticity of demand of commodity X if price of Y increases by LE10, given the same income level and same price of X? Interpret your answer. h) Find the change in consumption of good Y due to its price decrease to LE50. Then, decompose the total effect into the substitution and income effects. Show your steps and interpret results analytically and graphically. (Hint: Show all changes on the same diagram. Indicate at what values they intersect the budget lines) i) Given the sign of the substitution and income effects, what is the type of commodity Y
