Economics-AW-Q41 Online Services
#1. (20 marks) There are two goods in the economy – food F and light bulbs B (for the street lights around the residence). Edith’s utility is given by U F 4ln B , her income is $80 and prices are F P 8 and BP 4 .
(a) How much of each good will she consume if she has to purchase everything by herself? What is her utility level? Show her optimal consumption point on the graph.
(b) How much of each good will she purchase herself, if her neighbour provides B 6 and she can consume her neighbour’s street light without paying for it? What is her utility level? Add her new BL and new optimal consumption point to the graph in (a).
What effect or effects cause this change in Edith’s consumption from (a)?
(c) How much of each good will she purchase herself, if her neighbour still provides B 6 and she can consume street light without paying for it but the B P increases to $8? What is her utility level? On a separate graph show her new BL and new optimal consumption point along with her BL and optimal consumption point from in (b).
What effect or effects cause this change in Edith’s consumption from (b)?
#2. (19 marks) There is a monopoly producer of tablets facing the following demand Q 200 0.5P (where Q is # of tablets). Its cost is given by C 0.5Q2 .
(a) What will the equilibrium quantity and price of tablets sold by the monopolist? What are the profits?
(b) If the government impose an excise (per unit) of $25 on tablets, how do the equilibrium quantity and (consumer) price change? How much are the profits? How much of a tax is paid by the consumers? How much by the monopolist?
(c) If the government imposes an ad valorem tax of 25% instead of an excise tax, how do the equilibrium quantity and (consumer) price change? How much are the profits now?How much of a tax is paid by the consumers? How much by the monopolist? (HINT:we assume that the tax reduces MR not increases MC!).
(d) What is the reduction in the price received by the monopolist in (b) compared to (a)? What is it in (c) compared to (a)? Why is there such a difference in the price received by the monopolist between (b) and (c)? Which tax is better for the monopolist? Briefly explain. Which tax is better for the government? Briefly explain.#3. (18 marks) There are 2 sectors in the economy – food (F) and manufacturing (M). Assume that F F VMP 120 3L and M M VMP 240 L and the total number of workers in the economy is 200.
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(a) Use the differential taxation of inputs model to calculate the equilibrium split of workers between the industries and their wage.
(b) If the government decides to provide a $20 per worker subsidy in F sector, calculate the new equilibrium split of workers and new wage. Show the welfare change on the graph and calculate its value. Is it a gain or a loss?
(c) If instead the government provides a $20 per worker subsidy in F sector and at the same time impose a $20 tax per worker in M sector, calculate the new equilibrium split of workers and new wage. Show the welfare change on the graph and calculate its value. Is it a gain or a loss? Briefly explain why the equilibrium wage goes down compared to (a) even though the subsidy and the tax are of the same dollar amount.4. (13 marks) Malcolm’s preferences are given by
1 2 1 U 3F 3 M 3 l 3 , where F is food, M is manufacturing good and l is leisure per week. His total time endowment (after sleep) is 60 hours per week. Prices of F and M are $4 and $6 respectively. His hourly wage is $12.
(a) What is Malcolm’s weekly equilibrium consumption of goods and leisure? What is his weekly income? (HINT: you only need to use two tangency conditions.)
(b) If the government taxes his wage at the rate of 20%, what are his equilibrium consumption quantities? What is his after tax weekly income?
(c) If instead of the wage tax, the government mandates that leisure time should be fixed at its value in (a) and imposes a lump-sum income tax in the amount of $108. How does the new equilibrium here compare to the equilibrium in (b)? What can you say about the efficiency of the lump-sum? What about the wage tax in (b)? Briefly explain.
#5. (17 marks) Wendy consumes two goods Z and X, for which she has the following preferences,
U Z 8X2 . The prices of the goods are Z P 4 and XP 4 respectively and her
income is I 100 .
(a) Solve for Wendy’s optimal consumption bundle.
(b) If there is an ad valorem 0.25 on good Z, solve for her new optimal consumption bundle. Assume she bears the entire tax. Calculate her utility level.
(c) Calculate Wendy’s EV and EB due to the tax.
(d) Calculate the minimum ad valorem tax rate on good X above which Wendy will not consume good Z. Briefly explain if your result makes sense. #6. (8 marks) Provide short answers to the following questions.
(a) In Canada, economists are proposing a graduate tax system – those who want to earn a degree can do so without paying tuition but once they graduate and start earning salaries they will pay a flat rate tax (in addition to income taxes) for the rest of their lives. As this is expected to replace the student loans currently in existence, the revenue collected will be passed to universities. Briefly evaluate this tax from viewpoints of efficiency and horizontal equity.
(b) Your roommate and you are equally successful – you both graduated from the same university with the same degree in Economics. But you found a job with a higher annual salary than your roommate, and thus ended up paying larger amount in income taxes. Yet according to the utility definition of horizontal equity you come out as equally well off. Provide a couple of reasons how this would be possible. Given your analysis, is it fair for you to pay higher taxes?
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