2. (25 points) Carolina values consumption (c) and leisure (l). She has 16 units of time...

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2. (25 points) Carolina values consumption (c) and leisure (l). She has 16 units of time to divide between working or enjoying leisure. For each hour worked she receives 10 units of the consumption good. Suppose that Carolina's preferences are such that, she is willing to give up 2c/l units of consumption for an additional unit of leisure. Carolina also owns shares in a factory which gives dividend income of 16. The government in this economy taxes labour income only at a rate of 20% (i.e. T=0). a) Write down the budget constraint Carolina faces. Explain how she should determine consumption and leisure in order to maximize utility. b) Find the optimal choice of consumption and leisure and illustrate graphically. Explain why 6 units of labour is not an optimal choice. c) If everyone else in this economy has the same income and same preferences, and the total population is 50 people (including Carolina). What is GDP using the income approach and expenditure approach. d) If the government would like to increase government spending by raising the tax rate to 40%, how does this affect the optimal choice of consumption and leisure? Do you think GDP will rise or fall? e) Explain your result in d) in terms of income and substitution effects. Illustrate graphically. Which effect is the strongest in this case? 2. (25 points) Carolina values consumption (c) and leisure (l). She has 16 units of time to divide between working or enjoying leisure. For each hour worked she receives 10 units of the consumption good. Suppose that Carolina's preferences are such that, she is willing to give up 2c/l units of consumption for an additional unit of leisure. Carolina also owns shares in a factory which gives dividend income of 16. The government in this economy taxes labour income only at a rate of 20% (i.e. T=0). a) Write down the budget constraint Carolina faces. Explain how she should determine consumption and leisure in order to maximize utility. b) Find the optimal choice of consumption and leisure and illustrate graphically. Explain why 6 units of labour is not an optimal choice. c) If everyone else in this economy has the same income and same preferences, and the total population is 50 people (including Carolina). What is GDP using the income approach and expenditure approach. d) If the government would like to increase government spending by raising the tax rate to 40%, how does this affect the optimal choice of consumption and leisure? Do you think GDP will rise or fall? e) Explain your result in d) in terms of income and substitution effects. Illustrate graphically. Which effect is the strongest in this case?