Homework Assignment 4 ECON 103 ? Dr. Yan Li Department of Economics, UWEC These problems are due on Thursday, October 30, at the beginning of the class. Q1: Hotel rooms in New York go for $100, and 1000 rooms are rented on a typical day. To raise revenue, the mayor decides to charge hotels a tax of $10 per rented room. After the tax is imposed, the going rate guests have to pay for hotel rooms rises to $108, and the number of rooms falls to 900. Calculate the amount of revenue this tax raises for New York and the deadweight loss of the tax. Figure 1 Tax revenue = T x Q = 10 x 900 = $9,000 DWL = T x (Q1 ? Q2) x ½ = 10 x 100 x ½ = $500 The mayor now doubles the tax to $20. This price guests have to pay for hotel rooms rises to $116, and the number of rooms rented falls to 800. Calculate tax revenue and deadweight loss with this larger tax. Do they double, more than double, or less than double? (See the following figure for calculation.) Tax revenue = T x Q = 20 x 800 = $16,000 (less than double) DWL = T x (Q1 ? Q2) x ½ = 20 x 200 x ½ = $2,000 (more than double) Q2: Suppose the price of X (a good shown by x-axis) is $5, the price of Y is $10 and a hypothetical household has $500 to spend per month on goods X and Y. a. Sketch the household budget constraint. b. Assume that the household splits its income equally between X and Y. Show where the household ends up on the budget constraint. c. Suppose that the household income doubles to $1000. Sketch the new budget constraint facing the household. d. Suppose that price of X is now doubled to $10 and the price of Y is halved to $5. The income is still $500. Sketch the new budget constraint facing the household. Q3: The following table gives a hypothetical total utility schedule for the Cookie Monster. Calculate the Cookie Monster?s marginal utility schedule. 0 ? N/A 1 ? 100 2 ? 100 3 ? 75 4 ? 50 5 ? 25 6 ? 10 7 ? 0 Draw a graph of total and marginal utility. If cookies cost the Cookie Monster 5 cents each, what is the maximum number of cookies he would most likely eat? Q4: For this problem, assume that Joe has $80 to spend on books and movies each month. Movies cost $8 each, while books cost $20 each. Joe?s preference for movies and books are summarized by the following information: Movies Books No. per Month TU MU MU/P No. per Month TU MU MU/P 1 50 50 6.25 1 22 22 1.1 2 80 30 3.75 2 42 20 1 3 100 20 2.5 3 52 10 0.5 4 110 10 1.25 4 57 5 0.25 5 116 6 0.75 5 60 3 0.15 6 121 5 0.63 6 62 2 0.1 7 123 2 0.25 7 63 1 0.05 Fill in the figures for marginal utility and marginal utility per dollar for both movies and books. Are these preferences consistent with the ?law of diminishing marginal utility?? Explain briefly. Yes. Because the marginal utility decreases as the number of items bought per month increases. Given the budget of $80, what quantity of books and what quantity of movies will maximize Joe?s total utility? He will buy 5 movies and 2 books. PAGE \* MERGEFORMAT 1
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