Amal, a talented Afghan student living in the city of Balkh (one of the oldest cities...

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Amal, a talented Afghan student living in the city of Balkh (one of the oldest cities in the world), has to decide how to allocate her monthly budget m reserved for books, 21, and bus tickets, 22, that she uses when she visits her beloved grandmother Berezira. Amal's preferences can be represented by the utility function U (1₁,1₂)=₁ +4√/2 Let the price of a book be p₁ = 30 Afghani (which is Afghanistan's currency), the price of a bus ticket be p2 = 10 Afghani, and Amal's monthly budget reserved for books and bus tickets be m= 1050 Afghani. 1. What type of preferences Amal has over books and bus tickets? Explain your answer. 2. Calculate Amal's marginal rate of substitution, MRS, between books and bus tickets. Show your calculations. What is the economic meaning of the marginal rate of substitution? 3., 4. Derive Amal's uncompensated (Marshallian) demand functions for books, 21 (P₁, P2, m), and bus tickets, 22(P1, P2, m), respectively. Show your calculations (hint: for both an interior and corner solutions). 5. Given the prices and income above, derive Amal's optimal consumption bundle z (ri, i). Show your calculations. 6. Suppose that due to better economic conditions, the price of a book is now p₁ = 25 Afghani. Derive the new optimal bundle " = (x,z) showing your calculations. 7. Calculate and compare Amal's utility levels when she chooses z* and z", respectively. Briefly discuss if the change in Amal's utility level is what an economist would expect based on the rational choice model we have studied. 8. On a properly labeled graph, indicate books, 1, on the horizontal axis, and bus tickets, 12, on the vertical axis. Draw Amal's initial and new budget constraints, showing clearly the horizontal and vertical intercepts, and the slopes. Show Amal's optimal consumption bundles z and z" and a set of indifference curves (drawing 2 or 3 indifference curves is sufficient). Amal, a talented Afghan student living in the city of Balkh (one of the oldest cities in the world), has to decide how to allocate her monthly budget m reserved for books, 21, and bus tickets, 22, that she uses when she visits her beloved grandmother Berezira. Amal's preferences can be represented by the utility function U (1₁,1₂)=₁ +4√/2 Let the price of a book be p₁ = 30 Afghani (which is Afghanistan's currency), the price of a bus ticket be p2 = 10 Afghani, and Amal's monthly budget reserved for books and bus tickets be m= 1050 Afghani. 1. What type of preferences Amal has over books and bus tickets? Explain your answer. 2. Calculate Amal's marginal rate of substitution, MRS, between books and bus tickets. Show your calculations. What is the economic meaning of the marginal rate of substitution? 3., 4. Derive Amal's uncompensated (Marshallian) demand functions for books, 21 (P₁, P2, m), and bus tickets, 22(P1, P2, m), respectively. Show your calculations (hint: for both an interior and corner solutions). 5. Given the prices and income above, derive Amal's optimal consumption bundle z (ri, i). Show your calculations. 6. Suppose that due to better economic conditions, the price of a book is now p₁ = 25 Afghani. Derive the new optimal bundle " = (x,z) showing your calculations. 7. Calculate and compare Amal's utility levels when she chooses z* and z", respectively. Briefly discuss if the change in Amal's utility level is what an economist would expect based on the rational choice model we have studied. 8. On a properly labeled graph, indicate books, 1, on the horizontal axis, and bus tickets, 12, on the vertical axis. Draw Amal's initial and new budget constraints, showing clearly the horizontal and vertical intercepts, and the slopes. Show Amal's optimal consumption bundles z and z" and a set of indifference curves (drawing 2 or 3 indifference curves is sufficient).

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1 Amals preferences can be represented by the utility function Uxx x 4x Since the marginal utility of x is always 1 and the marginal utility of x is always decreasing as x increases Amals preferences ... View the full answer