Economics 1101 Lecture 042 Fall Semester 2007 Homework 3 ANSWER KEY Due October 24 2007 in Recitation 1 6 pts Suppose Lin produces oranges on an orange orchard the market demand for oranges and the fixed costs are given below a 3 pts Fill in the following chart Note that average and marginal costs as well as the marginal revenue should be given per orange not per 100 oranges Hint If demand is given by a function Q P then total revenue is given by P Q P Demand Oranges 0 100 200 300 400 500 600 b Q 750 5P Fixed Cost 500 500 500 500 500 500 500 Variable Cost 0 25 75 150 250 375 525 Fixed Cost 500 Total Cost 500 525 575 650 750 875 1025 AFC AVC ATC MC 5 00 2 50 1 67 1 25 1 00 0 83 0 25 0 38 0 50 0 63 0 75 0 88 5 25 2 88 2 17 1 88 1 75 1 71 0 25 0 50 0 75 1 00 1 25 1 50 Total Revenue 0 13000 22000 27000 28000 25000 18000 Marginal Revenue 130 90 50 10 30 70 1 pt Graph AFC AVC ATC and MC curves You can use one diagram 6 5 AFC AVC 4 ATC MC 3 2 1 0 0 c 100 200 300 400 500 600 1 pt How many oranges will the Lin choose to produce if she can only pick between the round numbers in the above table What are her profits 700 Maximum profit is when Lin produces 400 oranges if she is restricted to selecting hundreds of oranges This profit is When Q 400 P 150 400 5 150 80 70 So TR 70 400 28 000 TC 400 750 so the profit is 27 250 d 1 pt State 2 ways to find the quantity which yields the largest profit and explain why they give the same result The two methods are as follows 1 Calculate p directly TR TC then look for the quantity which gives the largest profit or smallest loss 2 Look for the largest quantity where MR MC as long as the market price is larger than the shut down price The first method is the direct way to find the largest profit The explanation for the second method is very intuitive Suppose Lin chooses 300 oranges But at 400 oranges she would still have MC 1 10 MR Then Lin could still make 10 1 100 dollars profit on those 100 oranges so her profit from only growing 300 oranges cannot be as large as possible In the same way if Lin chooses 500 oranges where MC 1 25 30 MR then she will save 1 25 30 100 dollars by not producing the last 100 oranges Since she can do better her profit cannot be a large as possible when she grows 500 oranges 2 6 pts 1 pt for each part except d and 2 pts for part d Suppose that the market for pocket books in St Paul is completely described by the following supply and demand curves S Q P 5 and D Q 25 2 P Here Q denotes the amount of books offered or demanded in thousands and P is the price of a book in dollars a Calculate the competitive equilibrium price and quantity on the market for pocket books Draw a diagram that illustrates the market and mark the equilibrium point Make S D to have 5 P 25 2P or P 10 so Q 5 15 P 14 13 12 11 10 9 8 7 6 5 4 Supply 3 Demand 2 1 Q 0 0 b 1 2 3 4 5 6 7 8 9 10 Calculate the consumer surplus CS producer surplus PS and the total surplus TS in the competitive equilibrium Mark these areas on the diagram you have drawn in part a CS 12 5 10 5 2 5 2 5 6 25 PS 10 5 5 12 5 TS CS PS 18 75 15 P 14 13 12 11 10 9 8 7 6 5 4 Supply 3 Demand 2 1 Q 0 0 1 2 3 4 5 6 7 8 9 10 Now suppose that the local government in St Paul decides to promote reading and states that books should be sold at a price that does not exceed 8 c What will be the quantity of books demanded at such price and how many books will actually be sold Illustrate your argument using a new diagram Qd 25 2 8 9 thousands Qs 8 5 3 thousands Hence only 3 thousand will be sold 15 P 14 13 12 11 10 9 8 7 6 5 4 Supply 3 Demand 2 1 Q 0 0 d 1 2 3 4 5 6 7 8 9 10 What are the new consumer surplus CS producer surplus PS and the total surplus TS after the government fixes the price Mark these areas on the diagram you have drawn in part c New CS 12 5 11 3 11 8 3 2 25 9 11 25 New PS 8 5 3 4 5 New TS New CS New PS 11 25 4 5 15 75 15 P 14 13 12 11 10 9 8 7 6 5 4 Supply 3 Demand 2 1 Q 0 0 1 2 3 4 5 6 7 8 9 10 Blue area is CS red is PS and green is DWL for the next part e Compare the two situations on the market in terms of the welfare of consumers and producers Who is now better off Who is now worse off Is the economy on the whole better off What is the Dead Weight Loss DWL Mark it on the diagram that you have drawn in part c Consumers are better off producers are worse off Economy on the whole is worse off DWL is 18 75 15 75 3 3 4 pts 1 pt each Consider the market for Easy Mac a Sketch a demand supply diagram for this market clearly labeling the equilibrium You may assume that demand and supply curves are linear P S E D Q You study survey data and observe that if Easy Mac costs 3 then 150 units of Ramen Noodles are demanded and if Easy Mac costs 4 then 250 units of Ramen are demanded b Calculate the cross price elasticity of demand for Easy Mac and Ramen Noodles Hint you need to pick out the relevant information from above How are these two goods related substitutes complements not related Use the cross price elasticity formula From the data you can only calculate the elasticity of demand for Ramen with respect to the price of Easy Mac pd RN EM 250 150 100 2 3 150 2 4 3 1 3 100 3 Therefore these goods are substitutes when price of Easy Mac goes up people switch to Ramen Noodles and demand for RN goes up c Suppose the price of Ramen decreases Draw and label the effects of this change on your diagram …