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IB9HP0
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UNIVERSITY OF WARWICK
Paper Details
Paper Code: IB9HP0
Paper Title: Data Management Exam
Exam Period: April 2024
Exam Rubric
Time Allowed: 2 hours
Exam Type: Standard Examination
Approved Calculators: Not Permitted
Instructions
This is a CLOSED book examination.
Read carefully the instructions on the answer book and make sure that the particulars
required are entered on your answer sheet.
The exam is structured in six parts. Each part is weighted as follows:
Part A 20 Marks
Part B 15 Marks
Part C 10 Marks
Part D 25 Marks
Part E 15 Marks
Part F 15 Marks
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Part A (20 Marks)
The following logical schema is provided for hospital management system:
patients (patient_id, name, date_of_birth, gender, address)
doctors (doctor_id, name, specialization, contact_number)
appointments (appointment_id, patient_id, doctor_id, appointment_date,
appointment_time)
medications (medication_id, name, dosage, instructions)
prescriptions (prescription_id, appointment_id, medication_id, quantity, frequency)
The fields with the suffix _id are either primary or foreign keys. Unfortunately, the
database developer hasn’t provided any input as to what is what.
a. Use your reasoning and explain for every logical table which attribute is a primary key and
which is a secondary key.
(2 Marks)
b. Provide the ER diagram (entities, attributes, relationships as well as the cardinality of the
relationships) based on the definition of the given keys provided on the logical schema.
(8 Marks)
c. Suppose the hospital decides to enhance its system to include information about medical
tests. Each patient may undergo multiple tests, and each test may involve one or more
doctors. Each test has a specific name, is ordered by a doctor for a patient and is executed
on a particular date. How does your ER diagram look after that
(5 Marks)
d. In addition to medical tests, the hospital wants to track the equipment used during these
tests. Each medical test may require one or more pieces of equipment, and each piece of
equipment may be used in multiple tests. How would you alter the logical schema to
capture that information Do you need to create new tables
(5 Marks)
(Part B over the page…/)
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Part B (15 Marks)
A logistics company manages various aspects of its operations using a database system. The
company has multiple warehouses located in different regions, each identified by a unique
Warehouse_ID. Each warehouse has attributes such as location, capacity, and manager. The
company also handles various products, each with a unique Product_ID. Products are stored
in the warehouses and have attributes such as name, category, and price. Additionally, the
company employs a team of drivers who are responsible for transporting products between
warehouses and to customers. Each driver is identified by a Driver_ID and has attributes like
name, contact information, and assigned truck. Customers place orders for products,
specifying the desired quantity and delivery address. Each order is assigned a unique Order_ID
and includes details such as order date, delivery date, and status.
a. Provide the E-R diagram depicting the entities and the relationships provided in the above
scenario using relationship sets.
(8 Marks)
b. Transfer the E-R diagram to a logical design. You need to explain how you translate the
relationship to the logical design.
(3 Marks)
c. Provide an SQL query to calculate the number of deliveries executed for each driver,
including drivers who haven’t executed any deliveries!
(4 Marks)
(Part C over the page…/)
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Part C (10 Marks)
The following table (TBL1) represents a hotel reservation system. The field room_id is the
primary key (highlighted in bold).
room_id room_type capacity price_per_night total_rooms available_rooms
001 Single 1 100 20 15
002 Double 2 150 25 20
003 Suite 4 300 10 5
004 Twin 2 130 30 25
005 Deluxe 2 200 15 10
006 Family 6 400 10 8
Provide the following SQL statements:
a. Calculate the average price per night for each room type for those rooms where the total
rooms are above 15.
(2 Marks)
b. Calculate the difference between the highest and lowest price per night for each room
type. Summarize these results by room type.
(3 Marks)
c. How many rooms are not available based on the information in TBL1
(3 Marks)
d. What is the room type with the least number of rooms on reservation (not available)
(2 Marks)
(Part D over the page…/)
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Part D (25 Marks)
The following table (expenses) is given.
customer_id customer_name order_id item_purchased item_price total_order_cost payment_method
1 John Smith 1001 Bread, Milk 2, 3 5 Card
5 John Smith on
behalf of John
Chen
1002 Eggs 2 2 Card
2 Emma Johnson 1003 Bread, Eggs 2, 2 4 Paypal
3 M. Lee 1004 Milk 3 3 Card
4 Sarah Kim 1005 Bread, Milk,
Eggs
2, 3, 2 7 Card declined,
used Cash
5 John Chen 1006 Various items NULL NULL Pending
… … … … … … …
a. Why is normalization important for these data What issues do we have with select,
insert, update and delete anomalies
(5 Marks)
b. Normalize the above table to another table (or tables) that correspond to the highest
possible normal form. Justify your answer, using functional dependencies.
(15 Marks)
c. Answer the following questions using the corresponding SQL statements
i. How many items have been bought in total
(2 Marks)
ii. What is the total order cost for all the orders in the normalized schema
(2 Marks)
iii. How many customers do we have in total
(1 Mark)
(Part E over the page…/)
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Part E (15 Marks)
The following table (SALES) is provided where the values represent the number of items sold
in a given two month period by year.
Product Category Year Jan-Feb Sales Mar-Apr Sales May-Jun Sales Jul-Aug Sales
Electronics 2021 2200 2900 3400 4100
Clothing 2020 1700 2100 2500 2900
Home Goods 2020 1300 1700 2100 2500
Electronics 2023 2400 3100 3600 4300
Clothing 2021 2000 2400 2800 3200
Home Goods 2021 1600 2000 2400 2800
a. Is SALES normalized If so, in which normal form Does it need to be transformed Explain
your answer using functional dependencies.
(5 Marks)
b. You are given the information that all columns apart from degree level and school year
are grades in a scale of 0 to 100 in four quantiles. The cells in these columns provide the
number of students (num_students). Name and describe the operation that you will
perform and what will the new table look like. Do you need to define any new keys
(5 Marks)
c. After transformation provide the SQL statement to calculate the difference between the
minimum and maximum grade for each degree level and year. Can this query be
executed If so, explain why. Is there an alternative way without transformation
(5 Marks)
(Part F over the page…/)
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Part F (15 Marks)
The following dplyr pipe sequence is given.
1 orders %>%
2 filter(order_status == “delivered”) %>%
3 left_join(order_items, by = “order_id”) %>%
4 group_by(customer_id) %>%
5 summarise(total_orders = n_distinct(order_id),
6 total_items = sum(quantity),
7 total_spent = sum(price * quantity)) %>%
8
9
filter(total_spent > 1000) %>%
arrange(desc(total_spent))
a. Provide the logical design equivalence from the dplyr pipe sequence.
(6 Marks)
b. Using the above pipe sequence, provide the SQL equivalent for the whole pipe sequence.
Explain your thought process in doing so.
(4 Marks)
c. Explain what will happen to the SQL output and the number of the records if line 8 is
modified as follows:
filter(total_spent > 1000 | total_spent < 800) Will the ordering of the records be the same Will that affect the results (5 Marks) End of Paper J) i. both & ii. excess demand K) i. both & ii. both L) i. both & ii. neither M) i. neither & ii. excess supply N) i. neither & ii. excess demand O) i. neither & ii. both P) i. neither & ii. neither Q3. In the 1980s, Robert Axelrod ran a series of computer tournaments based on a repeated prisoners’ dilemma. Let’s call the two players in a given game “Blue” and “Red”. If both players cooperate, they both receive the reward R for cooperating. If both players defect, they both receive the punishment payoff P. If Blue defects while Red cooperates, then Blue receives the temptation payoff T, while Red receives the "sucker's" payoff, S. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff S, while Red receives the temptation payoff T. The point scores that Axelrod used for these payoffs were: 0, 1, 3, and 5. But which payoff corresponds to which point score (Hint: you don’t need to have memorised the payoffs – you can reason this from the general structure of a prisoners’ dilemma.) A) = 0; = 1; = 3; = 5 B) = 0; = 1; = 5; = 3 C) = 0; = 3; = 1; = 5 D) = 0; = 3; = 5; = 1 E) = 0; = 5; = 1; = 3 F) = 0; = 5; = 3; = 1 G) = 1; = 0; = 3; = 5 H) = 1; = 0; = 5; = 3 I) = 1; = 3; = 0; = 5 J) = 1; = 3; = 5; = 0 K) = 1; = 5; = 0; = 3 L) = 1; = 5; = 3; = 0 Q4. A consumer with an income of consumes only two goods – and – available at prices and . Which of the following sets of changes might cause a parallel shift of the budget line i. rises; rises; rises ii. rises; falls; rises iii. rises; rises; falls iv. falls; falls; falls A) (i.) & (ii.) & (iii.) & (iv.) B) (i.) & (ii.) & (iii.) C) (i.) & (ii.) & (iv.) D) (i.) & (ii.) E) (i.) & (iii.) & (iv.) F) (i.) & (iii.) G) (i.) & (iv.) H) (i.) I) (ii.) & (iii.) & (iv.) J) (ii.) & (iii.) K) (ii.) & (iv.) L) (ii.) M) (iii.) & (iv.) N) (iii.) O) (iv.) P) None of (i.) to (iv.) Q5. Edith is walking through the countryside and she happens upon a Coke machine (the first one she’s seen for miles). She’s a bit thirsty and she realises that a good characterisation of her demand for coke would be the equation = 3 . At what price for a can will she buy exactly one can of Coke i. At a price of ￡2.25 per can, Edith will buy exactly one can ii. At a price of ￡1.75 per can, Edith will buy exactly one can iii. At a price of ￡1.25 per can, Edith will buy exactly one can iv. At a price of ￡0.75 per can, Edith will buy exactly one can A) i. is true, ii. is true, iii. is true, iv. is true B) i. is true, ii. is true, iii. is true, iv. is false C) i. is true, ii. is true, iii. is false, iv. is true D) i. is true, ii. is true, iii. is false, iv. is false E) i. is true, ii. is false, iii. is true, iv. is true F) i. is true, ii. is false, iii. is true, iv. is false G) i. is true, ii. is false, iii. is false, iv. is true H) i. is true, ii. is false, iii. is false, iv. is false I) i. is false, ii. is true, iii. is true, iv. is true J) i. is false, ii. is true, iii. is true, iv. is false K) i. is false, ii. is true, iii. is false, iv. is true L) i. is false, ii. is true, iii. is false, iv. is false M) i. is false, ii. is false, iii. is true, iv. is true N) i. is false, ii. is false, iii. is true, iv. is false O) i. is false, ii. is false, iii. is false, iv. is true P) i. is false, ii. is false, iii. is false, iv. is false Q6. Suppose you’re nearing the end of your degree and you’re looking for a job, and the job search is proceeding in the same way as the search problems we’ve worked on in tutorials. You think that your potential wage distribution is uniform on the interval (￡25 000, ￡35 000), and your first offer is for ￡31 000. If search is too costly, you should accept the current offer. But if searching is cheap enough (and you can delay saying ‘yes’ or ‘no’) then you should put the current offer on hold and search again. What is the maximum cost of search (in terms of cash, time, mental anguish, etc.) that you are willing to pay to get another job offer (Round your answer to the nearest ￡100.) A) ￡500 B) ￡600 C) ￡700 D) ￡800 E) ￡900 F) ￡1000 G) ￡1100 H) ￡1200 I) ￡1300 J) ￡1400 K) ￡1500 L) ￡1600 M) ￡1700 N) ￡1800 O) ￡1900 P) ￡2000 Q7. Psychologists Keith Stanovich and Richard West coined the terms System 1 and System 2 to reflect the dual processes seemingly at work in our mind. Evaluate the truth (or falsehood) of the following statements about them. i. System 1 is emotional ii. System 2 is rational iii. System 1 will only work if it is ‘switched on’ by System 2. A) i. is true, ii. is true, iii. is true, B) i. is true, ii. is true, iii. is false, C) i. is true, ii. is false, iii. is true, D) i. is true, ii. is false, iii. is false, E) i. is false, ii. is true, iii. is true, F) i. is false, ii. is true, iii. is false, G) i. is false, ii. is false, iii. is true, H) i. is false, ii. is false, iii. is false, Q8. Which of the following production functions is associated with straight-line isoquants when depicted in - space i. ( , ) = 2 + 3 ii. ( , ) = min [3 , 6 ] iii. ( , ) = 5 iv. ( , ) = 0.5 0.5 A) i & ii & iii & iv B) i & iii & iv C) i & ii & iv D) i & ii & iii E) ii & iii & iv F) i & ii G) ii & iii H) iii & iv I) i & iii J) i & iv K) ii & iv L) i M) ii N) iii O) iv P) None of i, ii, iii and iv Q9. Consider two firms: Firm Alpha is a small firm in a large city. Any reasonable amount of labour or capital that it might buy won’t affect the local price of either (i.e. the firm takes the prices of labour and capital as being fixed). What shape will this firm’s isocost curves be Firm Beta operates in labour and capital markets where bulk discounts are available on both factors of production: workers are hired via an agency, and the agency charges a bit less per worker the more workers are hired, and capital gets a similar discount for bigger quantities bought in (the discount is such that Beta always pays more in total when more labour or capital is bought in, but the per-unit cost does decline). What shape will Beta’s isocost curves be A) Alpha’s will be concave; Beta’s will be concave B) Alpha’s will be concave; Beta’s will be convex C) Alpha’s will be concave; Beta’s will be linear D) Alpha’s will be concave; Beta’s will be linear E) Alpha’s will be convex; Beta’s will be concave F) Alpha’s will be convex; Beta’s will be convex G) Alpha’s will be convex; Beta’s will be linear H) Alpha’s will be linear; Beta’s will be concave I) Alpha’s will be linear; Beta’s will be convex J) Alpha’s will be linear; Beta’s will be linear Q10. Suppose a competitive industry has the supply curve = 10 + 3Q. Suppose the market demand curve is = 50 5 . What is the producer surplus in this market (Round your answer to the nearest ten) A) 0 or less B) 10 C) 20 D) 30 E) 40 F) 50 G) 60 H) 70 I) 80 J) 90 K) 100 L) 110 M) 120 N) 130 O) 140 P) 150 or more Q11. The figure below shows a firm’s long-run total cost curve: Which of the following statements is (are) true if the prices of inputs are constant i. Long-run marginal costs are constant and equal to long-run average costs. ii. The firm’s production exhibits constant returns to scale. iii. The curve going through the origin indicates that only labour is used in production. A) i. is true, ii. is true, iii. is true, B) i. is true, ii. is true, iii. is false, C) i. is true, ii. is false, iii. is true, D) i. is true, ii. is false, iii. is false, E) i. is false, ii. is true, iii. is true, F) i. is false, ii. is true, iii. is false, G) i. is false, ii. is false, iii. is true, H) i. is false, ii. is false, iii. is false, Q12. Suppose a car park at the Trossachs National Park is run by a perfectly discriminating monopolist. The fixed costs are zero, and the marginal costs are constant and equal to ￡5. The market demand is given by = 1000 10P. What is the maximum per-period licence fee the government could charge the firm and have it stay in the business Round your answer down to the nearest ￡5,000. A) ￡30,000 or less B) ￡35,000 C) ￡40,000 D) ￡45,000 E) ￡50,000 F) ￡55,000 G) ￡60,000 H) ￡65,000 I) ￡70,000 J) ￡75,000 K) ￡80,000 L) ￡85,000 M) ￡90,000 N) ￡95,000 O) ￡100,000 or more Q13. Assess each of these three statements about the Hotelling’s location model where two ice cream vendors are free to position themselves wherever they wish along a straight beach: i. To minimise the average distance their clients have to travel, the vendors will choose to position themselves in the middle of the beach. ii. To minimise the average distance their clients have to travel, the vendors will choose to position themselves 1/4 and 3/4 of the way along the beach. iii. To minimise the average distance their clients have to travel, the vendors will choose to position themselves 1/3 and 2/3 of the way along the beach. iv. To minimise competitive pressure on the price of their ice creams both vendors will choose to position themselves at the opposite ends of the beach. A) i. is true, ii. is true, iii. is true, iv. is true B) i. is true, ii. is true, iii. is true, iv. is false C) i. is true, ii. is true, iii. is false, iv. is true D) i. is true, ii. is true, iii. is false, iv. is false E) i. is true, ii. is false, iii. is true, iv. is true F) i. is true, ii. is false, iii. is true, iv. is false G) i. is true, ii. is false, iii. is false, iv. is true H) i. is true, ii. is false, iii. is false, iv. is false I) i. is false, ii. is true, iii. is true, iv. is true J) i. is false, ii. is true, iii. is true, iv. is false K) i. is false, ii. is true, iii. is false, iv. is true L) i. is false, ii. is true, iii. is false, iv. is false M) i. is false, ii. is false, iii. is true, iv. is true N) i. is false, ii. is false, iii. is true, iv. is false O) i. is false, ii. is false, iii. is false, iv. is true P) i. is false, ii. is false, iii. is false, iv. is false . Q14. In your tutorial sheets on imperfect competition, there was a discussion of data on mark-ups based on the work of Jan De Loecker and Jan Eeckhout. Their data looked at country-level average mark-ups, where the mark-up for each country was calculated as the average mark-up of corporations whose headquarters were located in that country. Suppose (and this is controversial!) that the difference in markups arises from differences in market structure (i.e. not from e.g. the shape of marginal cost curves). Given this way of measuring mark-ups, what do you think about the following statements about the effects on domestic welfare of higher mark-ups (other things being equal): i. For the world as a whole, higher mark-ups will typically lead to lower worldwide welfare. ii. For small-open economies like Denmark, higher mark-ups will typically lead to lower domestic welfare. iii. For larger economies like the USA, higher mark-ups will typically lead to lower domestic welfare. A) i. is true, ii. is true, iii. is true B) i. is true, ii. is true, iii. is false C) i. is true, ii. is false, iii. is true D) i. is true, ii. is false, iii. is false E) i. is false, ii. is true, iii. is true F) i. is false, ii. is true, iii. is false G) i. is false, ii. is false, iii. is true H) i. is false, ii. is false, iii. is false Q15. Members of two groups, the blues and the greens, each have productivity values that range from ￡10 to ￡30/hr. Even though the ranges are the same, however, the averages are different: the productivity of the blues is ￡15/hr and the corresponding average for the greens is ￡24/hr. It is easy for anyone to see whether an individual is blue or green, and it is common knowledge that the group average productivities are ￡15/hr and ￡24/hr, but it is not easy to see how productive any individual is. A new productivity test has been devised though, and 1/3rd of the time it is able to give a correct measurement of an individual’s productivity, but the other 2/3rds of the time it gives random productivity value drawn from the relevant colour-group distribution. Employers are free to pay workers the productivity values that they expect. i. Assuming labour markets are competitive, how much will a blue with a test value of 18 be paid ii. Will a green with a test value of 18 be paid less, more, or the same amount as a blue who scores 18 A) i. ￡15/hr ii. less B) i. ￡16/hr ii. less C) i. ￡18/hr ii. less D) i. ￡22/hr ii. less E) i. ￡24/hr ii. less F) i. ￡15/hr ii. same G) i. ￡16/hr ii. same H) i. ￡18/hr ii. same I) i. ￡22/hr ii. same J) i. ￡24/hr ii. same K) i. ￡15/hr ii. more L) i. ￡16/hr ii. more M) i. ￡18/hr ii. more N) i. ￡22/hr ii. more O) i. ￡24/hr ii. more Q16. As noted in your tutorial sheets, the working age female labour force participation rate in Japan has risen sharply over the past decade, and has now overtaken the rate for the United States (which has been declining recently). You were asked to read an economist article explaining the reasons behind this trend. What reasons were given for the relatively high Japanese rate i. “Top down” cultural changes, with many women CEOs being appointed to top companies. ii. “Bottom up” cultural changes, with fewer women being slotted into lowly administrative jobs and being referred to as “office flowers”. iii. Japanese birth rates are declining, and this has left more time for women to work. iv. Japanese men do a lot of housework, and this has released time for women to work. A) (i.) & (ii.) & (iii.) & (iv.) B) (i.) & (ii.) & (iii.) C) (i.) & (ii.) & (iv.) D) (i.) & (ii.) E) (i.) & (iii.) & (iv.) F) (i.) & (iii.) G) (i.) & (iv.) H) (i.) I) (ii.) & (iii.) & (iv.) J) (ii.) & (iii.) K) (ii.) & (iv.) L) (ii.) M) (iii.) & (iv.) N) (iii.) O) (iv.) P) None of the above. Q17. Evaluate the following statements about general equilibrium in an exchange economy: i. A Pareto optimal allocation is one in which it is impossible to make one person better off without making at least one other person worse off. ii. In a pure exchange economy with only two consumers and two goods, for any given initial allocation of the two goods, a competitive exchange process will always exhaust all possible mutually beneficial gains from trade. iii. If consumers have convex indifference curves, any efficient allocation can be sustained as a competitive equilibrium. A) i. is true, ii. is true, iii. is true B) i. is true, ii. is true, iii. is false C) i. is true, ii. is false, iii. is true D) i. is true, ii. is false, iii. is false E) i. is false, ii. is true, iii. is true F) i. is false, ii. is true, iii. is false G) i. is false, ii. is false, iii. is true H) i. is false, ii. is false, iii. is false Q18. There are 40 natural history students in the village of Berik. They can either work part-time in a local book shop for ￡64 per day or give guided tours of local wildlife in the evenings. The income from the tours depends on how many of them offer their services and is given by = 112 4 2 , where L is the number of tour guides and T is daily income from tour guiding. The students prefer to give tours unless the job in the book shop pays more. Assess each of these three statements if the students decide individually whether to work in the book shop or give tours and their goal is to earn as much as possible: i. The number of tour guides will be double the socially optimal number of them. ii. Half of the students will choose to work in the book shop. iii. The number of students working in the book shop will be half the socially optimal amount. A) i. is true, ii. is true, iii. is true B) i. is true, ii. is true, iii. is false C) i. is true, ii. is false, iii. is true D) i. is true, ii. is false, iii. is false E) i. is false, ii. is true, iii. is true F) i. is false, ii. is true, iii. is false G) i. is false, ii. is false, iii. is true H) i. is false, ii. is false, iii. is false Q19. Consider a steel mill dumping waste into a loch where a salmon farm is located. The mill’s waste reduces the farm’s profit. The mill can install a filter system to reduce its waste, or the farm can pay for the installation of a water treatment plant. Their profits are presented in the matrix below (first number being the factory’s profit). Farm No treatment plant Treatment plant Mill No filter ￡400, ￡100 ￡400, ￡200 Filter ￡200, ￡500 ￡200, ￡350 Assess each of these three statements: i. The socially optimal outcome will be achieved even if the mill and the farm make their decisions individually (assuming they are both profit maximisers). ii. The socially optimal outcome will be reached if the mill has the property right to dump waste into the loch. iii. The socially optimal outcome will be reached if environmental regulations require the mill to install the filter. You should assume that the mill and farm make their decisions independently, and that negotiation between them is very costly/difficult (perhaps because the owners hate each other). When thinking about the social optimum in the context of this question consider only the information provided in the table and ignore all other considerations not mentioned here. A) i. is true, ii. is true, iii. is true, B) i. is true, ii. is true, iii. is false, C) i. is true, ii. is false, iii. is true, D) i. is true, ii. is false, iii. is false, E) i. is false, ii. is true, iii. is true, F) i. is false, ii. is true, iii. is false, G) i. is false, ii. is false, iii. is true, H) i. is false, ii. is false, iii. is false, Q20. A student society consisting of 20 economists, 20 sociologists, and 20 physicists is about to elect its next president. Arnold, Bo, and Chuck are the three candidates. Members of each group have the ranking schemes given in the table: Group Best Next best Last Economists Arnold Bo Chuck Sociologists Bo Chuck Arnold Physicists Chuck Arnold Bo The tradition in the society is to pit two candidates against each other and then pit the winner of that contest against the third candidate. How does the pairing that a person would wish for match up with their discipline i. Physicists should want round #1 to consist of Arnold vs. Bo ii. Sociologists should want round #1 to consist of Chuck vs. Bo iii. Economists should want round #1 to consist of Arnold vs. Chuck A) i. is true, ii. is true, iii. is true, B) i. is true, ii. is true, iii. is false, C) i. is true, ii. is false, iii. is true, D) i. is true, ii. is false, iii. is false, E) i. is false, ii. is true, iii. is true, F) i. is false, ii. is true, iii. is false, G) i. is false, ii. is false, iii. is true, H) i. is false, ii. is false, iii. is false, Section B – Written questions. Answer each question in a separate booklet. Answer all six questions. (60 points total — 10 points each) Written questions - Instructions You must write your answers to each of the questions in a separate booklet. You should write neatly and draw clearly – you cannot earn credit for answers that we cannot read. When deriving mathematical results, show your work – you will not earn full credit otherwise. If you make any important assumptions, state them clearly. Q21. If a set of indifference curves for two items are shaped like upward sloping convex curves, what does this mean Give an example. What does the slope of the line at any given point represent What about the intercept(s) [10 marks] Q22. All about elasticity… (a) Write down the standard equation for the price elasticity of demand. [1 mark] (b) Summarize the relationship between price elasticity, changes in price, and changes in total expenditure. [3 marks] (c) Why don’t we measure the responsiveness of demand to price changes by the slope of the demand curve instead of using the more complicated expression for elasticity [3 marks] (d) Why do long-run elasticities of demand differ from short-run elasticities [3 marks] Q23. Explain how a firm’s decision to either keep producing or to shut down is different in the short run and the long run. Which costs are most relevant and least relevant in each case Support your answer with a diagram or diagrams. [10 marks] Q24. When are the social costs of monopoly highest and when are they lowest Are the cases when the social costs are low (i.e. the social benefits are high) also cases where aggregate consumer surplus is high Support your answer with diagrams. [10 marks] Q25. On July 1 st Brewster won ￡10,500 in a lottery. According to the lottery’s terms and conditions he will be paid in two instalments, ￡3000 immediately and ￡7500 on August 1 st, and he must spend the prize by the end of August. Brewster has no other money before the end of August. Brewster’s utility function is ( 1, 2 ) = ln 1 + ln 2, where 1 and 2 represent his consumption of prize money in July and August respectively. Brewster’s bank offers him an incredibly generous deposit interest rate of 25% per month. The same interest rate applies if Brewster borrows from the bank. a) Write down Brewster’s budget constraint. [2 marks] b) Find the optimal values of 1 and 2. [5 marks] c) What would happen to the budget constraint if the interest rate decreased to 0% Illustrate your answer diagrammatically. [3 marks] Q26. When aggregating individuals’ preferences, in what circumstances should demand curves be summed horizontally and in what circumstances should they be summed vertically Explain, supporting your explanation with diagrams, giving a real-world example for each type. [10 marks]