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1. Imagine an individual who has the following Cobb-Douglas Utility function: U = $1 0.25 0.75 This person has an income of $70,000. Suppose the price of Good 1 (Vegetables) is p1 = 5 and the price of Good 2 (Meat) is p2 = 10. a) (10 marks) Determine the optimal consumption bundle for this individual. How much utility do they get from consuming this bundle? Construct a graph which illustrates this situation. b) (10 marks) Suppose that this person gets a promotion at work and their income increases to $80,000. What is this consumer's new optimal consumption bundle? Show whether this consumer is going to better off or worse off. Construct a graph which illustrates this situation. c) (15 marks) The government is concerned that people are eating too much meat and not enough vegetables. They are considering two policies: 1. A tax on meat equal to $2 per unit of meat consumed. 2. An income tax of $13,600, and a subsidy on vegetables of $1 per vegetable purchased. Answer the following questions for both of these policies. (Note: The income remains at the new higher value of $80,000) i) What is the new optimal consumption bundle? ii) What is the resulting utility of the consumer? iii) What is the net amount of money collected by the government? d) (5 marks) Based on your analysis, which of two policies would you recommend that the government pursue? Justify your answer.1. Imagine an individual who has the following Cobb-Douglas Utility function: U = $1 0.25 0.75 This person has an income of $70,000. Suppose the price of Good 1 (Vegetables) is p1 = 5 and the price of Good 2 (Meat) is p2 = 10. a) (10 marks) Determine the optimal consumption bundle for this individual. How much utility do they get from consuming this bundle? Construct a graph which illustrates this situation. b) (10 marks) Suppose that this person gets a promotion at work and their income increases to $80,000. What is this consumer's new optimal consumption bundle? Show whether this consumer is going to better off or worse off. Construct a graph which illustrates this situation. c) (15 marks) The government is concerned that people are eating too much meat and not enough vegetables. They are considering two policies: 1. A tax on meat equal to $2 per unit of meat consumed. 2. An income tax of $13,600, and a subsidy on vegetables of $1 per vegetable purchased. Answer the following questions for both of these policies. (Note: The income remains at the new higher value of $80,000) i) What is the new optimal consumption bundle? ii) What is the resulting utility of the consumer? iii) What is the net amount of money collected by the government? d) (5 marks) Based on your analysis, which of two policies would you recommend that the government pursue? Justify your answer.Problem 1 This is a non-math question about Ricardian equivalence. Imagine a two period economy with two types of agents: lenders and borrowers. Both have the same preferences and like to smooth consumption, but they differ in their income endowment of a perishable good. Lenders have a lot of income in the first period, and very little in the second. Borrowers have very little income in the first period but a lot in the second. There is a government who is running a balanced budget (taxing the same amount from both types). (a) If they can trade a riskless bond, who would lend to whom? (b) Now assume agents cannot borrow (can consume at most their after tax income). For whom is this constraint binding? Do you expect the interest rate to be higher or lower? The government now decides to lower taxes in the first period by A (keeping total expenditures fixed) (c) For a given interest rate, how does this affect savings for lenders? and for borrowers? and aggregate savings (including the government)? (d) What do you expect will happen to the equilibrium interest rate? Problem 2 Suppose that households change their preferences so that they wisk to work and consume more in each year. (a) Show graphically the effects of this change on the labor market. What happens to labor input L, and the real wage, "? (b) Show graphically the effects of this change on the market for capital services. What happens to the real rental price, ? What happens to the interest rate, i? (c) What happens to consumption, C, and investment, I? What happens over time to the stock of capital, K? Problem 3 Assume a one-time decrease in the capital stock, K, possibly caused by a natural disaster or war. Assume the population does not change. (a) Show graphically the effects of this change on the market for capital services. What happens to the real rental price, "? What happens to the interest rate, i? (b) Show graphically the effects of this change on the labor market. What happens to labor input L, and the real wage, F? (c) What happens to consumption, C, and investment, I? What happens over time to the stock of capital, K?Instructions: You may work on this problem set in groups of up to four people. Should you choose to do so, please make sure to legibly write each group member's name on the first page of your solutions. This problem set is due in class on Thursday February 15. 1. GLS, Chapter 8, Questions 1, 2, 4, and 5. 2. GLS, Chapter 8, Exercise 3. 3. Suppose that you have a standard two period consumption-saving problem. The household's objective is to maximize: max In C + 8 In C+1 s.t. Y4+1 1 + re (a) Use calculus to derive the Euler equation for this problem. Briefly provide some economic intuition for the Euler equation. (b) Combine the Euler equation from (a) with the intertemporal budget constraint to derive the consumption function (ie. an expression for C, as a function of parameters and variables which the household takes as given). What is the marginal propensity to consume? (c) Since saving is S, = Y - Ct, use your answer from (b) to derive an expression for the saving function (i.e. an expression for S, as a function of parameters and variables which the household takes as given). (d) We can define the saving rate as s = . Note that there is a time subscript on this, as, unlike the Solow model, the saving rate will not necessarily be constant. Derive an expression for the saving rate in this model. How does the saving rate move with the interest rate? What would have to be true about It+1 for the saving rate to be constant in this problem? (e) Take your answer from (d). Suppose that Yet1 = =Y, and that # =0.95. Suppose that re fluctuates between 0.00 and 0.10. What would be the maximum and minimum values of the saving rate? Given your answer, comment on whether the assumption of a constant saving rate in the Solow model is a bad assumption (there is no right or wrong answer here to what is "bad" - just discuss the question intelligently).Problem 1 This is a non-math question about Ricardian equivalence. Imagine a two period economy with two types of agents: lenders and borrowers. Both have the same preferences and like to smooth consumption, but they differ in their income endowment of a perishable good. Lenders have a lot of income in the first period, and very little in the second. Borrowers have very little income in the first period but a lot in the second. There is a government who is running a balanced budget (taxing the same amount from both types). (a) If they can trade a riskless bond, who would lend to whom? (b) Now assume agents cannot borrow (can consume at most their after tax income). For whom is this constraint binding? Do you expect the interest rate to be higher or lower? The government now decides to lower taxes in the first period by A (keeping total expenditures fixed) (c) For a given interest rate, how does this affect savings for lenders? and for borrowers? and aggregate savings (including the government )? (d) What do you expect will happen to the equilibrium interest rate? Problem 2 Suppose that households change their preferences so that they wisk to work and consume more in each year. (a) Show graphically the effects of this change on the labor market. What happens to labor input L, and the real wage, ;? (b) Show graphically the effects of this change on the market for capital services. What happens to the real rental price, ? What happens to the interest rate, i? (c) What happens to consumption, C, and investment, I? What happens over time to the stock of capital, K? Problem 3 Assume a one-time decrease in the capital stock, K, possibly caused by a natural disaster or war. Assume the population does not change. (a) Show graphically the effects of this change on the market for capital services. What happens to the real rental price, #? What happens to the interest rate, i? (b) Show graphically the effects of this change on the labor market. What happens to labor input L, and the real wage, "? (c) What happens to consumption, C, and investment, I? What happens over time to the stock of capital, K