Due 10/28/2008 at beginning of lectureEconomics 101 Homework #3 Fall 2008 Due 10/28/2008 at beginning of lecture Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework (legibly). Make sure you write your name as it appears on your ID so that you can receive the correct grade. Please remember the section number for the section you are registered, because you will need that number when you submit exams and homework. Late homework will not be accepted so make plans ahead of time. Please show your work. Good luck! Q1. Elasticity I. Price Elasticity of Demand: Amy’s demand for cheesecakes is Qd = 90 – 4P. a) At price P = 20, what is the price elasticity of demand? Hint: Use the point elasticity of demand formula to calculate this elasticity. εp = ______________. Is it elastic or inelastic at price P = 20? _______________ b) Calculate the price elasticity as the price moves from P0 = 20 to P1 = 15 by using the mid-point price elasticity formula (hint: this is the same formula as the arc elasticity formula). εp = ________________ c) Calculate the total revenue (TR) at P = 20 and P = 15 separately. When P = 20, TR = ___________; when P = 15, TR = __________________. Does the total revenue (TR) increase, decrease, or stay the same when the price decreases from P = 20 to P = 15? ________________. Use your calculation of the price elasticity of demand at these two different prices to explain the result in the change of total revenue. _____________________________________________________________________________________________________________________________________________________________________________________________________. d) At what price is the price elasticity of demand equal to 1? P = _____________ Page 1 of 9e) Complete the table below based on Amy’s demand for cheesecakes which is Qd = 90 – 4P. P Qdεp ⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛=QPslope1 TR (= P x Qd) 0 90 0 0 5 10 11.25 15 20 22.5 0 undefined 0 When the elasticity εp > 1: if the price increases, does the total revenue increase, decrease, or remain unchanged? _________. When the elasticity εp < 1: if the price increases, does the total revenue increase, decrease, or remain unchanged? _________. II. Cross-price elasticity of Demand: Amy substitutes cheesecakes for ice cream sometimes, but Amy always drinks coffee when she has a piece of cheesecake. f) The price of ice cream decreases by 10%. As a result, Amy’s demand for cheesecakes decreases from 11 cheesecakes to 9 cheesecakes. What is the cross-price elasticity of demand for Amy for these two goods? Hint: for this calculation just use the % change for price you have been given and then calculate the % change in the quantity demanded using the arc elasticity concept. εcheesecake p ice cream = _____________. From Amy’s perspective, is ice cream a substitute or a complement good for cheesecakes? ________________ Why? Use the concept of cross-price elasticity of demand to explain your answer. ____________________________________ g) The price of coffee increases by 20%. As a result, Amy’s demand for cheesecakes decreases by 15%. What is the cross-price elasticity of demand for Amy for these two goods? εcheesecake p coffee = _____________. From Amy’s perspective, is coffee a substitute or a complement good for cheesecakes? ________________ Why? Use the concept of cross-price elasticity of demand to explain your answer. ____________________________________ III. Income elasticity of Demand: Amy got a raise at work, and her income increases by 25%. As a result, her demand for cheesecakes increases by 15%. In the meanwhile, Amy’s demand for jelly decreases by 10%. Page 2 of 9h) What is Amy’s income elasticity of demand for cheesecakes? _____________ What does this income elasticity tell us about Amy’s valuation of cheesecakes (are cheesecakes normal or inferior goods)? ______________________ i) What is Amy’s income elasticity of demand for jelly? ____________________ What does this income elasticity tell us about Amy’s valuation of jelly (is jelly a normal or an inferior good)? ______________________ Q2. Tariffs and Quotas The domestic demand and domestic supply curves for MP3 players in a small closed economy are as follows: Supply: 23 +=SQPDemand: 102+−=DQP I. Closed Economy (no trade) a. Shade the area of consumer surplus (CS) and producer surplus (PS) of the economy without trade on Graph A below. Calculate the value of consumer surplus (CS) and producer surplus (PS) for the MP3 player market in this small closed economy. CS = ___________, PS = __________. Page 3 of 9II. Open Economy to Free Trade. Use the following information to answer question a) ~ d). Suppose that this small closed economy is open to free trade and that the world price is $62 per MP3 player. a. What is the quantity supplied by domestic producers? _______ b. What is the quantity demanded by domestic consumers? ________ c. With free trade, how many MP3 players will the country import or export? _____ d. Shade the area of the consumer surplus (CS) and producer surplus (PS) after the economy opens to free trade on Graph B above. Calculate the value of consumer surplus (CS) and producer surplus (PS). CStrade = _________ and PStrade = ___________. Page 4 of 9III. Open Economy to Trade (with Tariff) Use the following information to answer question a) ~ i). Suppose that the government imposes a tariff of $6 on each imported MP3 player, and the world price is $62 per MP3 player. a. What is the quantity supplied by domestic producers after the introduction of the tariff? ___________________. b. What is the quantity demanded by domestic consumers after the introduction of the tariff? ___________________. c. How many MP3 players will the country import or export after the introduction of the tariff? ________________. d. Shade the areas of the consumer surplus (CS), the producer surplus (PS), the total tariff revenue (TR), and the dead weight loss (DWL) after the introduction of tariffs on Graph C above. Page 5 of 9e. Calculate the value of consumer surplus (CS) and the value of producer surplus (PS) for the MP3 player market after introducing the tariff. CS w/Tariff = __________ and PS w/Tariff = ____________. f. Calculate the value of total tariff
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