Tutorial 2 - Slutsky Equation PDF

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Slutsky Equation...

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Tutorial 2: The Slutsky Equation and Inter Temporal Choice 1. Thirsty Ed drinks only pure spring water but he can purchase it in two different containers: 0.75 litre and 2 litres. Because the water is identical, he regards these two goods as perfect substitutes. a) Assuming Eds utility depends only on the quantity of water consumed and that the containers themselves yield no utility, express this utility function in terms of 0.7 litre containers (x) and 2-liter containers (y). b) State Eds demand function for x in terms of px , p y ∧ I . c) How do changes in I and p y shift the demand curve for x. d) What would the compensated demand curve for x look like in this situation? 2. Suppose the utility function for good x and good y is given by:

U ( x , y )=xy+ y a) Calculate the uncompensated (Marshallian) demand functions for x and y and describe how the demand curves for x and y are shifted by changes in I and the price of the other good. b) Calculate the expenditure function for x and y c) Use the expenditure function calculated in part b) to compute the compensated demand functions for goods x and y. Describe how the compensated demand curves for x and y are shifted by changes in income or by changes in the price of the other good. 3. Peregrine Pickle consumes ( c 1 , c 2 ) and earns ( m 1 , m 2 ) in periods 1 and 2 respectively. Suppose the interest rate is r. (a) Write down Peregrine's intertemporal budget constraint in present value terms. (b) If Peregrine does not consume anything in period 1, what is the most he can consume in period 2? (c) This is the (future value, present value) of his endowment.??????? (d) If Peregrine does not consume anything in period 2, what is the most he can consume in period 1? (e) This is the (future value, present value) of his endowment.??????? (f) What is the slope of Peregrine's budget line? 4. Decide whether each of the following statements is true or false. Then explain why your answer is correct, based on the Slutsky decomposition into income and substitution effects. (a) "If both current and future consumption are normal goods, an increase in the interest rate will necessarily make a saver save more (b) "If both current and future consumption are normal goods, an increase in the interest rate will necessarily make a saver choose more consumption in the second period."...