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Homework 1 This problem set (PS) is due at 6pm on Thursday, February 10

Economics

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Homework 1 This problem set (PS) is due at 6pm on Thursday, February 10. The maximum score is 100 points. Be sure to review the syllabus for details about homework assignments and their grading! Feel free to contact me via e-mail if you have specific questions about the HW assignment. Note that some exercises have several parts, and each part may conceal more than one task for you. Be sure to answer every question thoroughly for full credit! Exercise 1 (30 points) Assume an economy in which only apples and oranges are produced. In year 1, 500 million pounds of apples are produced and consumed and its price is $0.50 per pound, while 300 million pounds of oranges are produced and consumed and its price is $0.80 per pound. In year 2. 400 million pounds of apples are produced and consumed and its price is $0.60 per pound, while 350 million pounds of oranges are produced and its price is $0.85 per pound (a) Using year 1 as the base year, calculate the GDP price deflator in years 1 and 2, and calculate the rate of price change between years 1 and 2 from the GDP price deflator (b) Calculate the growth rates of the nominal and real GDP (using different base years). Why do you obtain different results in the real GDP growth rate with different base years? Explain Exercise 2 (30 points) In year 1 and year 2, there are two products produced in a given economy, smartphones and earphones. Suppose that there are no intermediate goods. In year 1, 4,000 smartphones and 2.000 earphones are produced and sold at $2,000 and $200 each, respectively. However, due to an earthquake in year 2. some production lines are destroyed and the production of smartphones and earphones falls to 1,000 and 1,500 units, respectively. However, the price of each pair of smartphone doubled and the price of each pair of earphones increased to $300. (a) Calculate nominal GDP for year 1 and year 2. (6) Calculate real GDP in each year and the percentage change in real GDP from year I to year 2 tsing year 1 as the base year. (c) Calculate the implicit GDP price deflator and the change in the deflator from year 1 to year 2 using year 1 and year 2 as the base years, respectively. (d) Suppose that the design and quality of smartphones improved significantly in year 2. For example, the battery life of smartphones in year 2 was twice as long in year 1. Discuss how this quality improvement may affect real GDP through the output and the price level. Exercise 3 (40 points) Consider a consumer who is endowed with h = 24. The consumer faces a real wage rate w = 4, dividends # = 7 and taxes T = 3. (a) Write down the formulae for the budget and the time constraints. (b) What is the price of leisure here? (e) Draw the budget constraint. (d) Redraw the budget constraint when w goes up to 5. (C) Suppose wis again equal to 4. Redraw the budget constraint when I goes down to 2.