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3. Shannon lives in Dublin in 1845 and loves spending her Sunday mornings at the city's market finding the best meatloaf (M) and potatoes (T) in town. Her preferences are represented by the following utility function: M2 U(T, M) = 100T T2 + M + 2 In 1845, the price of 1 pound of meatloaf is 1 shilling, and the price of 1 pound of potatoes is also 1 shilling. Shannon makes a weekly income of 55 shillings. (a) Write down the expression for Shannon's budget constraint l1 in 1845. (b) Compute her marginal rate of substitution between potatoes and meatloaf. (c) Solve for her optimal shopping basket at the Dublin city market in 1845. 60 Meatloaf (M) 40 30 gut 20 1845 12 U1. 10 U2 1848 li 0 0 10 20 30 40 50 60 Potatoes (T) The next year, Ireland is hit by the Great Famine, which will last 3 years in total. By 1848, the price of potatoes has increased by 10% to 1.1 shillings for one pound. However, the price of meatloaf and Shannon's income have remained constant. (d) Write down the new budget constraint l2 of Shannon in 1848. (e) Compute her new shopping basket at the Dublin market in 1848. A year after, the newly-elected Irish government decides to give a one-time transfer to all Irish households in order to study the behavior of consumers during the period of the Great Famine. This transfer is designed in a such a way that people can afford a basket equally desirable as the one pre-Famine (1845), while making sure that prices stay the same as those in 1848. The conclusion of the Irish Ministry of Budget is that, under this program (1.8), people like Shannon decide to buy exactly 42 pounds of potatoes, and 12 pounds of meatloaf (gut). (f) Explain how to identify the income and the substitution effects from the graph, and compute them numerically for potatoes. Which effect is dominating? (g) What are these types of goods called? 3. Shannon lives in Dublin in 1845 and loves spending her Sunday mornings at the city's market finding the best meatloaf (M) and potatoes (T) in town. Her preferences are represented by the following utility function: M2 U(T, M) = 100T T2 + M + 2 In 1845, the price of 1 pound of meatloaf is 1 shilling, and the price of 1 pound of potatoes is also 1 shilling. Shannon makes a weekly income of 55 shillings. (a) Write down the expression for Shannon's budget constraint l1 in 1845. (b) Compute her marginal rate of substitution between potatoes and meatloaf. (c) Solve for her optimal shopping basket at the Dublin city market in 1845. 60 Meatloaf (M) 40 30 gut 20 1845 12 U1. 10 U2 1848 li 0 0 10 20 30 40 50 60 Potatoes (T) The next year, Ireland is hit by the Great Famine, which will last 3 years in total. By 1848, the price of potatoes has increased by 10% to 1.1 shillings for one pound. However, the price of meatloaf and Shannon's income have remained constant. (d) Write down the new budget constraint l2 of Shannon in 1848. (e) Compute her new shopping basket at the Dublin market in 1848. A year after, the newly-elected Irish government decides to give a one-time transfer to all Irish households in order to study the behavior of consumers during the period of the Great Famine. This transfer is designed in a such a way that people can afford a basket equally desirable as the one pre-Famine (1845), while making sure that prices stay the same as those in 1848. The conclusion of the Irish Ministry of Budget is that, under this program (1.8), people like Shannon decide to buy exactly 42 pounds of potatoes, and 12 pounds of meatloaf (gut). (f) Explain how to identify the income and the substitution effects from the graph, and compute them numerically for potatoes. Which effect is dominating? (g) What are these types of goods called
