epartment of Economics rof. Kenneth Train University of California, Berkeley Fall 2011 1) a) ECONOMICS 1 roblem Set 1 Suggested Answers Grapes (thousands) 125 115 A B 95 C 70 40 E 0 0 200 400 600 800 1000 F Llamas b) The opportunity cost of these 200 llamas is the number of bushels of grapes that you must forgo in order to get these 200 llamas. If you weren t producing any llamas, you could produce 125,000 bushels of grapes. Now you are producing only 115,000. So the opportunity cost of these 200 llamas is 10,000 bushels of grapes. c) The F is bowed outward due to the law of increasing opportunity costs. Imagine you are producing at point A in the graph of part a). There you produce only grapes using all of your land. Now you want to consider raising 200 llamas (which means moving to point B). To raise llamas, you must allocate some land for grazing by the llamas and can t produce grapes on that part of your land. Since llamas graze equally well on any kind of land, you will allocate the areas that are least good for grapes, that is, the rocky, hilly areas; production of grapes will be reduced by only 10,000 bushels. But suppose now that you are producing at point and want to increase your production of llamas by 200 again. You will have to allocate more land to the grazing of the llamas, probably some of the flat loamy areas since you are already producing 600 llamas. Those areas are better for producing grapes and the reduction in the production of grapes is larger: it goes from producing 70,000 bushels to only 40,000. The opportunity cost of these additional 200 llamas is now 30,000 bushels of grapes, 3 times larger than before. Since the slope of the F represents this opportunity cost, its shape shows that the higher the production of llamas (good on the x-axis) the higher the number of bushels of grapes (good on the y-axis) you 1
must forgo to produce some additional number of llamas; that is, the higher the opportunity cost of llamas in terms of grapes. If you draw the line tangent to points B and E in your graph, you will see that the second line is steeper than the first, which means that the slope is higher, showing higher opportunity costs. d) Given your current production levels (point B), the opportunity costs of producing 200 more llamas is 20,000 bushels of grapes (you go from producing 115,000 bushels to producing only 95,000). That is, if you produce 200 more llamas you must produce 20,000 fewer bushels of grapes. The 200 extra llamas would increase your revenues by $24,000 ($120 each times 200). The 20,000 fewer bushels of grapes would mean that you earn $20,000 less revenue from grapes ($1 for each bushel). Since $24,000 exceeds $20,000, you would make more revenue ($4000 more revenue to be exact) by producing 200 more llamas and 20,000 fewer bushels of grapes. You have just figured out that you will make more revenues by shifting your production toward more llamas and less grapes (that is, by moving along the F toward point C). Should you go beyond point C to point? No. At point C, the opportunity cost of 200 more llamas is 25,000 bushels of grapes. If you produced another 200 llamas your revenues from llamas would increase by $24,000; however, your revenues from grapes would fall by $25,000. Overall you would earn less revenue. So you will be better off by producing (and selling) at point C. If you still don t believe me, calculate total revenues at each point and you ll find that: Revenues oint A $125,000 oint B $139,000 oint C $143,000 oint $142,000 oint E $136,000 oint F $120,000 e) The new table will be: Llamas Grapes 0 137,500 200 126,500 400 104,500 600 77,000 800 44,000 1,000 0 2
The graph looks like this: Grapes (thousands) 125 115 95 70 A A B B C C E 40 E 0 F Llamas 0 200 400 600 800 1000 Notice that the point F remains the same: when you don t produce grapes, the largest amount of llamas you can get is still 1,000. This should be obvious since the improved method is for production of grapes and not of llamas. If you don t produce any grapes, you don t get the advantages of the new method. However, at any other point except F you can get more of both goods even though the improved technology is used in only one sector. The reason for this is as follows: to produce a certain amount of grapes, you need less land now that you did before, so you can use the rest of the land (previously used to produce grapes) for the grazing of more llamas, thus increasing the production of llamas. Also notice that the amount of land available to you is the same. There was a technological change that made this shift of the F possible. 2) a) 6 Fish 60 Coconuts 3
b) The opportunity cost of one fish is the amount of coconuts Robinson could be collecting if he were not fishing. It takes him an hour to catch one fish (a lousy, fisher, no doubt). Since he can collect 10 coconuts per hour, the opportunity cost of one fish is 10 coconuts. c) If you drew the graph asked in part a), you may have already noticed that the F on this island economy is a straight line instead of being bowed outward. The reason is that there is only one factor of production: Robinson s time (labor). If you remember the explanation in part c) of problem 1, we said that the reason for the bowed out shape was the existence of two different kinds of land (two factors of production). In this island economy, to produce one more fish costs Robinson the same hour, which always translates into 10 coconuts. The law of increasing opportunity costs does not apply here: regardless of how much of both goods Robinson is producing, the opportunity cost of one more fish will always be 10 coconuts (1 hour of labor). Also, that is why in part b) we could compute the opportunity cost of one fish without setting a specific point for our calculation. In summary, the law of increasing opportunity costs applies when there is more than one factor of production, each being better suited to produce one good than the others. 3) a) Since some people were probably eating oat bran because of this alleged characteristic, they will quit eating it and the demand curve will shift leftward (a decrease in demand). There is no change in the supply curve. Both the equilibrium price and the quantity of oat bran sold will be lower. S 1 1 2 2 2 1 4
b) This is an increase in the cost of producing vegetables. For each quantity produced, agricultural producers will require a higher price (to cover the higher cost) in order to be induced to supply that quantity. Because of this, the supply curve will shift upward (a decrease in supply). There is no change in the demand curve. The equilibrium price will rise and the quantity of vegetables sold will decrease. S 2 S 1 2 1 2 1 c) Since it takes some time to build a house even when prices go up, we can think of the supply of housing at any point in time as being vertical (short term supply of housing). ue to the earthquake, the stock of houses was reduced by 10% and the supply curve shifts to the left (a decrease in supply). There is no change in the demand curve. The equilibrium price of housing will go up and the quantity of housing sold will go down (by 10%). S 2 S 1 2 1 2 1 5
d) As in part c), the supply of coffee is reduced, increasing the price of coffee. Therefore some coffee drinkers will find it too expensive to drink and will switch to its substitutes, one of which is tea. The demand for tea will increase (the demand curve for tea shifts to the right) and there is no change in the supply curve of tea. Both the equilibrium price of tea and the quantity of tea sold will increase. S 2 S 1 Coffee S Tea 2 2 2 1 1 1 2 1 1 2 4) a) What you observe in the real world (rising output and falling prices) are not points on the supply curve, but equilibrium points, that is, intersections of a supply curve and a demand curve. The observation is perfectly valid with an upward sloping supply curve that is shifting downward (or to the right) showing lower costs of production and/or technological improvements. When the supply curve shifts to the right, the equilibrium points will move along the demand curve, showing lower prices and higher output produced and sold. S 1970 S 1980 S 1990 70 80 90 E 70 E 80 E 90 70 80 90 b) The low rents in Berkeley are forced by the rent control here, creating an excess demand for housing that will be unattended. These people will have to go to neighboring communities to get an apartment, increasing the demand for housing in there above the level that it would normally have. If prices are low in these communities, the reason is not rent control in Berkeley. 6
c) The city revenues for illegal parking equal the fine times the amount of illegal parking. If fines are doubled and the amount of illegal parking is reduced, then total revenues for the city will increase by less than double. We could even think of a situation in which doubling the fines makes them so expensive that only the rich can afford to park illegally and the amount of illegal parking will drop by a lot, say more than 50%. In this case, the city revenues from illegal parking will drop. d) Opportunity costs are not always measured in monetary terms. The retired person doing volunteer work could have been doing something else (like reading, sleeping, or going to the movies) instead of volunteering. These forgone activities constitute the opportunity cost for the retired person of doing volunteer work. 5) a) We can view the demand curve as showing the maximum price consumers are willing and able to pay for each amount. Because of the government policy, consumers will be able to pay a higher price (twice as much, in fact) for each quantity since the government is paying half of it. For example, if consumers were willing to pay $10 per unity for 100 units, now they ll be willing to pay $20 for the same 100 units. They will in fact be paying only $10, since the government is paying 50% of the market price. That will rotate the demand curve clockwise, that is, the new demand curve will be shifted to the right, but it will be steeper. 2 S 2 1 1 1 2 b) The equilibrium quantity of the drug sold will increase. c) As you can see in the graph in part a), the equilibrium price will increase so producers will obtain more money per unit sold. d) robably not, since the government is paying 50% of the new equilibrium price, which is higher than before. 7