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PS3 Page 1 of 5 Economics 150.001 American University Spring 2020 Problem Set 3 ** DUE: IN CLASS, THURSDAY FEBRUARY 27, 2020 ** Instructions: 1. For Problems 1 and 3: Please provide your answers on a separate sheet (or sheets) of paper. (There is not enough room on the Problem Set pages themselves to provide full answers.) 2. For Problem 2: For parts (a) through (d) you may either print out the table in the file “PS3 Problem 2 Handout” and enter your answers there, or reproduce the tables in that handout on a separate sheet (or sheets) of paper. For part (e), draw your answer on a separate sheet of paper. 3. For questions asking you to “explain your answer”, you must provide an explanation of your answer to be eligible for full credit. 4. Please try to write neatly and be sure to indicate clearly all information you wish to be considered as part of your answer. 5. Please staple or paper clip your submission before coming to class. 6. Please write your name AND University ID# on your problem set before handing it in. PROBLEM 1 (35 POINTS) The countries of Utopia and Dystopia can each produce two goods: wine and cars. If Utopia produces only wine, it can produce 80 barrels per year; if it produces only cars, it can produce 40 cars per year. If Dystopia produces only wine, it can produce 60 barrels per year; if it produces only cars, it can produce 90 cars per year. a. Draw Utopia’s Production Possibilities Frontier (PPF), making sure to label the axes. (You may assume that Utopia’s PPF is a straight line.) Choose any 4 points on the PPF and indicate how many cars and how many barrels of wine Utopia is producing at those points. b. Draw Dystopia’s PPF, making sure to label the axes. (You may assume that Dystopia’s PPF is a straight line.) Choose any 4 points on the PPF and indicate how many cars and how many barrels of wine Dystopia is producing at those points. c. Which country has the Absolute Advantage in producing wine? Which country has the Absolute Advantage in producing cars? Page 2 of 5 d. Indicate the opportunity cost of producing cars and wine in Utopia and Dystopia by reproducing the table below on your answer sheet and filling it in. (Note: the opportunity cost of producing a barrel of wine will be in units of cars, and the opportunity cost of producing cars will be in units of barrels of wine.): Utopia Dystopia Barrel of Wine Car e. Which country has Comparative Advantage in producing wine? Which country has Comparative Advantage in producing cars? Explain your answers, using the concept of opportunity cost. f. Suppose the two countries decided to trade with each other. If each country wants to take maximum advantage of the potential gains from trade, how many cars and barrels of wine should each produce? g. Demonstrate that each country can gain from trade by proposing a specific trade that would allow each country to consume a combination of cars and barrels of wine that would have been infeasible without trade. (Note: there are many possible correct answers.) Specifically, fill in the blanks in the statement below: Utopia sends __________ to Dystopia in return for ________ . After the trade, Utopia has ________ barrels of wine, and ________ cars; and Dystopia has ________ barrels of wine and ________ cars. PROBLEM 2 (35 POINTS) Maria consumes only two goods: pens and notebooks. Currently, pens cost $1 each and notebooks cost $3 each. Maria’s income is $15. The tables below show the total utility Maria receives from consuming various quantities of each of the goods: Quantity of Notebooks Total Utility Quantity of Pens Total Utility 0 0 0 0 1 75 1 40 2 135 2 60 3 185 3 75 4 230 4 87 5 270 5 97 6 300 6 105 7 320 7 111 Page 3 of 5 Access the file “PS3 Problem 2 Handout” which is posted in the “Problem Sets” folder on Blackboard. For the following questions, you may either print out the handout and write your answers directly on the printout or you may reproduce the tables contained in the handout on a separate piece of paper and write your answers in there. a. Fill in the blank cells in Tables 1 and 2 depicted in “PS3 Problem 2 Handout”. b. Using Table 3, calculate the optimal consumption bundle for Maria. (Note: for full credit you must provide the correct quantities of pens and notebooks AND fill in as much of Table 3 as was necessary to arrive at your answer.) The store where Maria buys her supplies announces a sale on notebooks, dropping their price to $2 each. Print out (or draw) a new set of blank tables for parts (c) and (d) below. c. Fill in the blank cells in Tables 1 and 2 d. Using Table 3, calculate the optimal consumption bundle for Maria now, with the new lower price for notebooks. (Note: for full credit you must provide the correct quantities of pens and notebooks AND fill in as much of Table 3 as was necessary to arrive at your answer.) e. You now have enough information to plot two points on Maria’s demand curve for notebooks. Draw a graph of those two points. PROBLEM 3 (30 POINTS) A consumer, Sylvia, has income of $40. She consumes only two goods, books and sandwiches. Currently, the price of each book is $10 and the price of each sandwich is $5. In Figure 1 on p. 5, her budget line is labeled “BL1” and her initial optimal consumption point is labeled “A”. a. Sylvia’s income increases (while the prices of books and sandwiches remain the same), resulting in a shift in her budget line to BL2. Based on the diagram, what is Sylvia’s income now, after the increase? b. Consider points B, C and D, and answer the following questions, explaining your answer each time. (Note: no credit will be given for answers without explanations) i. Which of the points could be Sylvia’s new optimal consumption point if both books and sandwiches are normal goods? ii. Which of the points could be Sylvia’s new optimal consumption point if books are normal goods and sandwiches are inferior goods? iii. Which of the points could be Sylvia’s new optimal consumption point if books are inferior goods and sandwiches are normal goods? *** (CONTINUED ON NEXT PAGE…) *** Page 4 of 5 Now, return to the original situation, where Sylvia’s income is $40, the price of a book is $10, the price of a sandwich is $5 and Sylvia’s optimal consumption point is “A”. c. Suppose the price of sandwiches falls to $4, and assume that both sandwiches and books are normal goods for Sylvia. Reproduce the table below on a separate sheet of paper and fill it in to indicate what the substitution effect, income effect and overall effect of the price change will be. Specifically, in the cells in the table below you will be indicating in which direction demand for the two goods will change as a result of the substitution and income effects of the price change, and also what will be the overall effect on demand for the two goods. If the effect will be to increase demand, enter a “plus” symbol (+). If it will be to decrease demand, enter a “minus” symbol (–). If the effect will be ambiguous, enter a question mark (?). Substitution Effect Income Effect Overall Change in Demand Demand for Sandwiches Demand for Books d. Repeat the analysis of part (c) (i.e. draw and fill in another table indicating the substitution, income and overall effects of the price change), but this time assume that books are an inferior good and sandwiches are a normal good. e. Repeat the analysis of part (c) (i.e. draw and fill in another table indicating the substitution, income and overall effects of the price change), but this time assume that sandwiches are an inferior good and books are a normal good. Page 5 of 5 Figure 1. Sylvia’s Budget 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Nu m be r o f S an dw ich es Quantity of Books A B C D BL1 BL2