Econ 1 - Problem Set 2 With Solutions

Problem Set 2 Hard copies of your answers are due at the beginning of your section, either on Thursday, October 6, or Friday, October 7. For example, if your section starts at 10:00am on Friday, you should submit your answers to your TA in your section classroom at 10:00am on Friday, October 7. Late problems earn zero points. Note: you can work on these problems or your own, or in a small group with other current Econ 1 students. If you choose to work in a group, each student needs to hand in a separate, individual copy to his/her TA. 1. The meal plan at university A lets students eat as much as they like for a fixed fee of $500 per semester. The average student there eats 250 pounds of food per semester. University B charges $500 for a book of meal tickets that entitles the student to eat 250 pounds of food per semester. If the student eats more than 250 pounds, he or she pays extra; if the student eats less, he or she gets a refund. If students are rational, at which university will average consumption be higher? Why? 2. A price-taking (that is, competitive) firm makes air conditioners. The market price of one of their new air conditioners is $120. Its total cost information is given in the following table. Air conditioners/day 1 2 3 4 5 6 7 8

Total cost ($/day) 100 150 220 310 405 510 650 800

How many air conditioners should the firm produce per day if its goal is to maximize its profits? 3. Tofu was available 30 years ago only from small businesses operating in Chinese quarters of large cities. Today tofu has become popular as a highprotein health food and is widely available in supermarkets throughout the United States. At the same time, production has evolved to become factory-

based using modern food-processing technologies. Draw a diagram with demand and supply curves depicting the market for tofu 25 years ago and the market for tofu today. Given the information above, what does the demand-supply model predict about changes in the volume of tofu sold in the United States between then and now? What does it predict about changes in the price of tofu? 4. 1Consider a firm that has a fixed cost of $60. Complete the following table. Output 1 2 3 4 5 6

FC

VC $10 $18 $30 $45 $65 $90

TC

MC

AFC

AVC

ATC

5. 2You want to know the short-run marginal cost of producing a Chevrolet Caprice. Comment on the following statement from an analyst in the production department: “The marginal cost of a Caprice, given our current volume, is $12,500. Of course, the actual marginal cost depends on the number of cars produced. The larger the number produced, the lower the unit cost because we will spread out our design and tooling costs over more cars.”

1

From Economics, Principles and Tools by Arthur O’Sullivan and Steven Sheffrin. Fourth edition. Pearson/Prentice Hall. 2006. 2 ibid.

Extra practice problems (completely optional; no points awarded) A. Economists have observed that in times of low unemployment there are fewer business startups, while in times of high unemployment more people decide to start their own businesses. Verbally explain this observed behavior in terms of opportunity costs. B. On October 7, 2003, CNN reported that British “researchers found that classical music […] was the most successful in encouraging people to part with their cash [in restaurants], with diners spending more than 24 pounds (US$40) a head.” “With no background music, spending [in meals] fell to around 21 pounds (US$35).” (a) Graphically show the market for restaurant food when no restaurant plays any music. Make sure you include demand and supply curves, and show the equilibrium price and quantity. (b) Now suppose that all restaurants start playing classical music, at no additional cost to the restaurant. How would the market for restaurant food look like after this change? Starting from the same diagram you drew in part (a), make sure you include demand and supply curves after the introduction of classical music, and show the new equilibrium price and quantity. (c) After complaints from the Recording Industry Association of America (the trade group that represents the U.S. recording industry), restaurants have to start paying for playing classical music during meals. Graphically show the effects in the market for restaurant dinners, and, separately, in the classical music market. Make sure you include demand and supply curves, and show the equilibrium prices and quantities in each market (one graph per market). C. Madagascar is one of the main producers and exporters of vanilla, the plant used in food and drink flavoring. In 2000 and 2001, storms destroyed much of Madagascar’s vanilla production. (a) Graphically show the world market for vanilla before and after the storms. Make sure you include demand and supply curves, and show the equilibrium prices and quantities. You can assume the vanilla market is competitive. (b) By 2002 most of the effects of the storms on vanilla production were over, and the market was back to normal. However, later that year Coca Cola announced its vanilla flavored Coke. Graphically show the world market for vanilla after the introduction of the vanilla Coke. Make sure you include demand and supply curves, and show the equilibrium prices and quantities. (c) Briefly explain how the effects on price and quantity are different in part (a) and part (b). Would you be able to tell the two initial shifts apart just from observing prices and quantities? What is the key piece of information?

Economics 1 HW# 2 Solution Set 1. Consider the demand curve for food by college students. In particular, suppose that the demand curve is downward sloping (this denotes a decreasing marginal benefit of food. In the graph that follows, I will assume the demand curve is linear purely for convenience). At University A, there is an unlimited supply of food at a price of $500. Students must pay a fixed fee of $500 regardless of how much they consume. Thus at University A, the price of an extra pound of food is zero. On the other hand, students at University B do not face a fixed fee. While they pay $500 at the beginning of the year to eat 250 pounds of food, they will get a refund/bill if they choose to eat less/more than the 250 pounds, and they actually face a price of $2 per pound. Given these prices, students at University A will continue eating until their marginal benefit is zero while students at University B will stop eating sooner, when their willingness to pay for an additional pound of food is $2. This can be seen in the following graph:

2. Recall from class that a firm maximizes profit by producing the largest quantity such that marginal cost is less than or equal to the price received for each quantity. To answer this question, I propose adding a marginal cost column to the table given in the question. Since the price is $120, then the firm will maximize profits by selling 6 air conditioners per day. One can verify this by calculating the total profits for each unit. Augmenting the table with columns for Total Revenue and Profit yields:

Air conditioners/day

Total Cost

Total Revenue (P*Q)

Profit

Marginal Cost

1 2 3 4 5 6

100 150 220 310 405 510

120 240 360 480 600 720

20 90 140 170 195 210

??∗ 50 70 90 95 105

7 8

650 800

840 960

190 160

140 150

*We do not know the fixed cost associated with the production of air conditioners, therefore we cannot know the marginal cost of producing the first unit. 3. An increase in the popularity of protein as a source of protein is the same as an increase in the demand for tofu, or an upward shift of the demand curve. Advancement in technology for producing tofu is the same an increase in the supply of tofu. This is the same as a rightward shift in supply. Graphically,

Clearly, the quantity of tofu sold in the US has increased. However, it is not clear what will happen to the price of tofu. The supply expansion is putting downward pressure on the price while the demand expansion is putting upward pressure is putting pressure on the price. Whether price goes up, down, or stays the same cannot be determined because the question does not tell us the size of the demand and supply shifts, which is needed to determine this.

4. Your table should look like this. Recall that total cost is equal to the FC plus the sum of variable costs up to each unit. Output 1 2 3 4 5 6

FC 60 60 60 60 60 60

VC 10 18 30 45 65 90

TC 70 78 90 105 125 150

MC 10 8 12 15 20 25

AFC 60 30 20 15 12 10

AVC 10 9 10 11.25 13 15

ATC 70 39 30 26.25 25 25

5. Marginal cost is the change in total costs due to a one unit change in the quantity produced. In the short run we know that some factors of production are fixed. The analyst tells us that the given the current production volume, the marginal cost is $12,500. He adds that if the volume were larger then the marginal cost would be lower too. This is untrue. Given that the factors involved in producing a Caprice are fixed in the short run, it is not possible to lower marginal cost because the costs of things like tooling and design are spread out over a larger quantity. Tooling the machines and designing the car are fixed costs. It is true that the average total cost would decrease for the reasons mentioned by the analyst, but marginal cost would remain the same in the short run. Larger numbers of Caprices reduce the average fixed cost component of the average total cost. Extra Problems A. Opportunity cost is defined as “the value of the next-best forgone alternative that was not chosen because something else was chosen” (Taylor, p. 5). The question tells us that in times of low unemployment there are fewer startups than in times of high unemployment. We are asked to explain this phenomenon in terms of opportunity cost. From the question we can conclude that it must be that the opportunity cost to starting a business during times of low unemployment must be higher than in times of high unemployment (note: higher (opportunity) costs implies fewer startups here). Next we need to find what these opportunity costs are and compare them. There are many opportunity costs involved with starting your own business. The money you have to invest in your business and the foregone income (i.e. wages and fringe benefits) from not working for an already established firm are two examples of opportunity costs associated with starting your own business. To answer the question, we need to know which of these opportunity costs will vary with the level of unemployment (because any opportunity cost that is the same in both scenarios will not influence your decision to start a business). If you are unemployed, you don’t earn any income from an already established firm, which means that this opportunity cost goes down to zero. Since the amount of money you would need to invest into your new business should not change much with the level of unemployment we can

assume it to be the same (yes, workers might ask for a lower wage, but that is not an opportunity cost for you, but a cost to your potential startup). Hence, during times of high unemployment many people face relatively low opportunity costs of starting their own businesses. Similarly, during times of low unemployment most people have jobs and thus face relatively high opportunity costs. The lower the opportunity cost to starting their own business, the more likely it is that somebody will actually start one. Thus, we can conclude that there will be more business startups when there is high unemployment (lower opportunity costs) than when unemployment is low (higher opportunity costs). B. (a) The initial market before classical music looks like this.

Price (per person)

Restaurant food without classical music

S

P*=35

D

Q*

Quantity (number of diners)

(b) The problem states that when restaurants play classical music, spending (in meals) increased from $35 to $40 per head. So if a restaurant starts playing music at no additional cost, we can say that the demand for restaurant food increases, as people spend more time at the restaurant, eat more and end up paying more. The demand curve shifts up, and there is a movement along the supply curve, resulting in a higher equilibrium quantity and price ($40).

Price (per person)

Restaurant food with classical music

S

P2=40 P1=35

D’ D

Q1

Quantity (number of diners)

Q2

(c) Making restaurants pay for playing classical music during meals is the same as increasing the cost of one of its production inputs. Thus the restaurant now faces increased costs and as a result supply shifts up. There is a movement along the new demand curve, D', resulting in a lower equilibrium quantity and higher price of food supplied.

Price (per person)

Restaurant food with costly classical music

S’ S P3 P2=40

D’

Q3

Q2

Quantity (number of diners)

Once restaurants are forced to pay in order to play classical music it means that new consumers have entered the market. As a result, demand for classical music increases, shifting the demand curve up. There is a movement along the supply curve, resulting in increased Q and P.

Price

Market for classical music

S

P’ P

D’ D

Q

Q’

Quantity

C. (a) The storm destroying much of the production leads to a decrease in the amount of available vanilla at every possible price. This can be represented as a shift left in the supply curve. This shift leads to a movement along the demand curve to the new equilibrium. The result is an increase in price and decrease in quantity sold.

Price

Effects of the storms on the vanilla market

S’

S P’

P

D

Q’

Quantity

Q

(b) The introduction of Vanilla Coke will result in a need for more vanilla at every possible price. This can be represented as a shift right in the demand curve. This shift leads to a movement along the supply curve to the new equilibrium. The result is an increase in price and in quantity sold.

Price

Effects of the Vanilla Coke on the vanilla market after storms have passed

S

P’ P

D’ D

Q

Q’

Quantity

(c) In part a, we experienced a shift in the supply curve which led to an increase in price and a decrease in quantity sold. In part b, we saw a shift in the demand curve, leading to an increase in both price and quantity sold. Even if one were only able to observe the changes in price and quantities, it would still be possible to distinguish between these two shifts because the equilibrium quantity shifts in opposite directions. An increase in both price and quantity implies a shift right in demand while an increase in price accompanied by a decrease in quantity implies a shift left in supply.