1. Each month, Katie spends Em on bananas. Her supermarket sells two types of bananas: Fairtrade (F) and non-Fairtrade bananas (N). Fairtrade bananas cost PP = 23/kg while non-Fairtrade bananas cost PN = El/kg. Katie's Marginal Rate of Substitution between the two types of bananas is constant along all the indifference curves and given by: dF MRSN.F = dNV = -1/2 (a) What does this indicate for Katie's preferences for Fairtrade and non-Fairtrade bananas? In particular: are these goods perfect substitutes, perfect complements or imperfect substitutes? Explain why. (3 points) (b) Draw a couple of Katie's indifference curves, with N on the horizontal axis. Make sure you label your graph carefully. Write down the mathematical expression of a utility function representing Katie's preferences for Fairtrade and non-Fairtrade bananas. (4 points) (c) Derive Katies' demands for Fairtrade and non-Fairtrade bananas that solve her utility maximisation problem. (6 points) (d) Draw the Engel curves for Fairtrade and non-Fairtrade bananas (with income m on the vertical axis). Make sure you label your graph carefully, including giving the intercept and the slope of the Engel curves. (6 points) (e) Assume that her income is m = $12. How many kilos of Fairtrade and non-Fairtrade bananas will Katie purchase at the optimum? (2 points) (f) Now, assume that the production of Fairtrade bananas is subsidized such that their price PF changes from Pg to P. = $1.5/kg (the price of non-Fairtrade bananas and the income remain unchanged: Py = 1 and m - 12). Compute the change in demand for good F. What is the proportion of this total effect that is due to the Slutsky substitution effect? (7 points) (Please turn over) (g) Assume that the government decides to increase the level of the subsidy such that now P= = PN = 1. Compute the change in demand for good F due to the price change from Pp to P. What is the proportion of this total effect that is due to the Slutsky substitution effect? (7 points)