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Econ 301 – F07 ANSWERS to PROBLEM SET 1 - due in class on Tuesday September 11 Wissink 1. Argentina and Brazil both produce leather and coffee with labor. The labor input is measured in hours, coffee is measured in gallons and leather is measured in yards. The table below shows labor requirements to produce a unit of coffee and of leather in each country. (It is assumed that the labor requirements per unit of output in production remain the same irrespective of the quantity of the two goods produced.) Each country has 120 hours of labor available, which can be allocated between the two activities. Labor can not go from one country to the other but coffee and leather can. HOURS REQUIRED 1 gallon of coffee 1 yard of leather Argentina Brazil 10 hrs 15 hrs 4 hrs 20 hrs a. Graph the production possibilities frontier (PPF) for both Argentina and Brazil (separately) clearly labeling the axes. (Note: The labor requirements per unit of output remain constant irrespective of the quantity produced.) [ANSWER] LArgentina = LBrazil = 120 hours Argentina's PPF Leather (yards) (e)(0,8) 8 9 (d)(6,4) 4 Brazil's PPF Leather (yards) 6 (d)(15,3) 3 0 (e)(30,0) 0 0 12 24 Coffee (gallons) 0 15 Coffee (gallons) 30 b. What is the opportunity cost of producing an extra gallon of coffee in Argentina? In Brazil? [ANSWER] The opportunity cost of producing an extra gallon of coffee = the marginal opportunity cost of producing coffee in terms of leather (MOC) Argentina: MOC of Coffee is 2/3 (yards of leather/1 gallon of coffee) Brazil: MOC of Coffee is 1/5 (yards of leather/1 gallon of coffee) c. What is the opportunity cost of producing an extra yard of leather in Argentina? In Brazil? [ANSWER] Argentina: MOC of Leather is 3/2 (gallons of coffee/1 yard of leather) Brazil: MOC of Leather is 5 (gallons of coffee/1 yard of leather) d. Suppose that both Argentina and Brazil are self sufficient i.e., they each rely on their own production for their consumption and do not trade with each other. Also assume that each nation devotes exactly a half of its total labor availability to the production of coffee and the rest to the production of leather. Indicate the combination of coffee and leather produced and consumed in each country on the graphs of part (a). [ANSWER] see the graph in (a). Argentina devotes 60 hours of its labor in producing coffee and 60 hours of its labor in producing leather. 10 hours are used to produce 1 gallon of coffee. 60/10 = 6 gallons of coffee is consumed in Argentina, and 60/15 = 4 yards of leather. The combination of coffee and leather produced and consumed in Argentina is (Coffee, Leather) = (6 gallons,4 yards). Brazil produces 15 gallons of coffee with 60 hours of its labor and 3 yards of leather with 60 hours of its labor. The combination for Brazil is (Coffee, Leather) = (15 gallons, 3 yards). e. Suppose each country devotes all its labor availability to the production of the commodity in which it has a comparative advantage (i.e., a relatively lower opportunity cost). Indicate the production point of each country after specialization. Again use graphs for part (a). [ANSWER] see the graph in (a). Argentina specializes in producing leather. All 120 hours are used to produce leather and the production point of Argentina is (Coffee, Leather) = (0 gallon, 8 yards). Brazil specializes in producing coffee. All 120 hours are used to produce coffee and the production point of Brazil is (Coffee, Leather) = (30 gallons, 0 yard). f. Show that the two countries could now exchange coffee for leather so that the consumption point of both countries (after specialization and exchange) lies outside of their own PPFs. Give a specific example. [ANSWER] see the graph in (a). For example, Argentina produces 8 yards of leather. Brazil produces 30 gallons of coffee. They agree to an exchange where Argentina gives Brazil 3.5 yards of leather in exchange for 8 gallons of coffee. So Argentina would consume 4.5 yards of leather and 8 gallons of coffee and Brazil would consume 3.5 yards of leather and 22 gallons of coffee. Note that both countries are consuming MORE of both coffee and leather as compared to their consumption point in part (d) and that both countries are consuming bundles that are outside their individual PPFs. That is to say, if Argentina made 8 gallons of coffee for itself, it could only have 2.67 yards of leather. And if Brazil made 22 gallons of coffee for itself it could only have 1.6 yards of leather. g. Suppose we add Uruguay to the picture with 60 hours of labor and with an input requirement of 5 hours of labor for each unit of coffee and 5 hours of labor for each unit of leather. How would this alter the joint PPF assuming we look at all three countries? [ANSWER] Argentina (A) Brazil (B) Uruguay (U) 1 gallon of coffee 10 hrs 4 hrs 5 hrs 1 yard of leather 15 hrs 20 hrs 5 hrs * MOC of coffee 2/3 yards 1 yard 1/5 yards (the middle) (the smallest) (the largest) MOC of leather 3/2 gallons 5 gallons 1 gallon (the middle) (the largest) (the smallest) Maximum 12 gallons in coffee, or 30 gallons in coffee, or 6 12 gallons in coffee, or Production Rates 8 yards in leather yards in leather 12 yards in leather NOTE: MOC represents the marginal opportunity cost. - Now see graph… 2 The Joint PPF U and A specialize in leather production, B varies. Leather (yards) 28 U specializes in leather production, B specialize in coffee production, and A varies. 21 A specializes in leather production, B varies. 14 B specializes in coffee production, A varies. 7 A and B specialize in coffee production, U varies. 0 0 10 20 30 40 50 Coffee (gallons) The joint PPF expands. h. Assuming a market with only these three countries as suppliers of coffee, construct the coffee supply curve based on the principle of comparative advantage. [ANSWER] Quantity of Coffee Relative Price of Coffee 0 gallons 0 yards 30 gallons 1/5 yards 42 gallons 2/3 yards 54 gallons 1 yard Who is Producing Coffee No country Brazil Brazil, Argentina Brazil, Argentina, Uruguay Supply Curve for Coffee Relative Price yards) 1.2 Brazil, Argentina, Uruguay 1 0.8 Brazil, Argentina 0.6 0.4 Brazil 0.2 0 0 10 20 30 40 50 60 Coffee (gallons) 2. Consider the following two equations that describe market activities in the Cortland NY tire market. Let X = number of tires per month and P = price per tire 3 Equation A: X=500-2P Equation B: X=-25+P a. Which equation would represent the demand curve and why? [ANSWER] Equation A would represent the demand curve. The slope of the price, -2, is negative. It describes that the quantity demanded of tires (XD) decreases when the price (P) increases. b. Which equation would represent the supply curve and why? [ANSWER] Equation B would represent the supply curve. The slope of the price, 1, is positive. It describes that the quantity supplied of tires (XS) increases when the price (P) increases. c. Find the market equilibrium price and number of tires traded, i.e., P* and X*. [ANSWER] At the market equilibrium, XD=XS, 500-2P = -25+P. => 525=3P => P* = 175 and X*=150. d. Graph the equilibrium and label your graph carefully. [ANSWER] Demand Curve: X=500-2P / Supply Curve: X=-25+P S P (per tire) 250 P1=212.50 P*=175 Surplus=112.5 P0=100 0 D 0 Xquota=75 X*=150 187.5 250 500 X (number of tires per month) e. Suppose there was a quota placed on this market. What set of values for the quota would make the quota binding? [ANSWER] The quantity quota, Xquota, must be below X* to be binding. Thus, any Xquota in the range of (0,150) would make the quota binding. f. Suppose the quota is set at Xquota= 75. Carefully and completely describe the consequence of this quota on both demanders and suppliers. Show its effect in your diagram. [ANSWER] Sellers would produce Xquota=75 with the price, P0=100, but could sell tires with the price, P1=212.5 since the demand for tires would be willing to pay up to the price, P1=212.50 with Xquota=75. The supply is really the original supply curve up to X=75 and then supply becomes vertical at X=75. Thus, the new equilibrium price is higher than P*=175. See the graph in (d) 4 g. Suppose Ima Smart insists that a better policy is to impose a price floor that is set equal to the market price you would get with the quota. Analyze Ima's suggestion using your graph and the demand and supply equations. [ANSWER] Suppose that the price floor imposed is P1=212.50. At P1=212.50, sellers want to sell 187.5 (XS=-25+P1=-25+212.50=187.5), but buyers only want to buy 75 (XD=500-2P1=5002*212.50=75). There is a surplus of 112.50=187.5 - 75. See the graph in (d). h. Suppose that INSTEAD OF THE QUOTA the mayor of Cortland decides to place a per unit tax of $5.00 per tire on each tire sold. The mayor decides to collect the tax revenue from the suppliers of tires. Determine the new market situation and figure out how much demanders now pay and how much suppliers now receive per tire after all is said and done (that is after all tire taxes are paid). What side of the market would you say seems to have “eaten” relatively more of the tax and why? [ANSWER] The tax will be collected from the suppliers. After the tax, the suppliers’ “market” supply curve is PS=30+X (note it’s best to add the $5 tax directly to the INVERSE supply curve). At the new equilibrium, newPS=oldPD, 30+X* = 250 – 1/2X* => 1.5X* = 220 newX*=146.67 and newPD=176.67. So the demanders pay 176.67 per a tire and the suppliers receive 171.67 (which is 176.67 minus the tax of 5) per tire. Note that suppliers have the relatively higher economic price incidence. That is to say they “eat” 175-171.67 = $3.33 of the tax while demanders only “eat” 176.67-175 = $1.67 of the tax. 3. Consider a particular service - your choice. Listed below are some events that could have some effect on one or more of the following with respect to that service: quantity demanded, quantity supplied, demand, and supply. Indicate which of the above four are directly affected and in what direction (i.e., increase, decrease, etc.). Let’s consider the education service of private schools. a. The service becomes more fashionable. [ANSWER] There is an increase in demand for the education service. The demand curve shifts right. 5 b. An income tax is levied on consumers. [ANSWER] Income decreases as an income tax is imposed. Assuming the good is normal, which is probably is in this case, a decrease in income decreases the demand for the education service. The demand curve shifts left. c. There is a rise in the price of an essential input used in production of the service. [ANSWER] The rise in the cost of providing the education service decreases supply. The supply curve shifts left. d. The price of the service itself changes. [ANSWER] An increase in the price of the education service decreases the quantity demanded, and increases the quantity supplied. A decrease in the price of the education service increases the quantity demanded, and decreases the quantity supplied. e. The price of a close substitute (substitute in consumption) increases. [ANSWER] Suppose that the price of the education services of public schools increases. Since private education and public education are substitutes in consumption, demand for private education will increase, i.e., shift to the right. 4. Before market reforms were initiated in the Soviet Union back in 1991, prices were often set by the government. a. Explain, with the aid of a graph, why there were lines for ordinary consumer goods, such as soap. [ANSWER] At the market equilibrium, the equilibrium price is P* and the equilibrium quantity demanded and supplied is X*. But when the government set the price as P0 < P*, there is a market shortage, X0D-X0S. The quantity demanded is higher than the quantity supplied. Price S P* P0 0 0 X0S X* X0D Quantity b. In October, 1990, the Soviet government announced that soap prices would double as of January 1, 1991. In the days just following the announcement soap lines increased. Explain how this could have happened. [ANSWER] In October, 1990, the price of soap is P0. When the government announced, people knew that the price of soap would double after 3 months, January 1, 1991. People would be willing to buy more than the amount that they needed with cheaper price. Thus, the demand for soap increased in 1990 if they expect prices to really increase sharply in 1991. 6 5. Suppose the supply function of apples in Upstate New York is: XS = 20 + 2PX – 3Y + 4Z where X refers to apples. If the supply for apples also depends on fertilizer, which variable to do you think is the price of fertilizer, Y or Z? Why do you think so? [ANSWER] Y would be the price of fertilizer. Fertilizer is an input to produce apples. The coefficient of Y, -3, in the supply function is negative. It implies that when the price of fertilizer increases, the suppliers would want to produce fewer apples. 6. Suppose that the demand for pork is QD = 286 – 20P where P is the price of pork. Suppose that the supply for pork is: QS = 178 + 40P – 60Ph where P is the price of pork and Ph is the price of hogs. Mathematically, how does the equilibrium price of pork vary as the price of hogs changes if the variables that affect pork demand are held constant at their “ceteris paribus” values? [ANSWER] At equilibrium, QD=QS 286-20P*=178+40P*-60Ph 60P*=286-178+60Ph=108+60Ph P*=108/60+Ph Then, P*=1.8+Ph From the equation above, the equilibrium price of pork (P*) has a positive relation to the price of hogs (Ph) and in fact the derivate of P* with respect to Ph = 1, so for every incremental change in the price of hogs there is an equal incremental change in the eq. price of pork. 7. Use a demand and supply diagram to explain the statement, “Talk is cheap because supply exceeds demand.” At what price is this comparison being made? [ANSWER] Let’s consider the market for Talk. The graph shows that “talk is cheap,” i.e. its market price is zero and that at this price, quantity supplied exceeds quantity demanded. Note that this is not the ONLY correct answer, you might have some similar answer that makes essentially the same point. Price S D P*=0 QD QS Quantity 7