LUBS2140
Intermediate Microeconomics
Semester Two 2022/2023
Section A - Answer all questions
200 words per question
Question 1
Figure 1 shows a utility function for an individual. What are the individual’s risk preferences? Explain your answer.
Figure 1
(10 marks)
Question 2
Table 1 shows the proportion of UK adults that are smokers, the average price of a pack of cigarettes and the mean income (adjusted for inflation) in the UK for the last 20 years. You are working as an economist for the Government Economic Service and you have been asked to consider what measures can be used to reduce the proportion of cigarette smokers. Use the data in Table 1 and what you know about Marshallian demand to make and explain your recommendations. Is there any other data that you would request in addition to the below?
Table 1: UK Cigarettes Smokers, Cigarette Prices and Income.
|
Year
|
Proportion of
cigarette
smokers (All
persons aged
16 and over)
|
RPI: Average
price -
Cigarettes 20
king size filter
|
Mean real equivalised
household disposable
income of individuals
(adjusted for CPI)
|
|
2021
|
12.7
|
1152
|
38994
|
|
2020
|
14.5
|
1111
|
39218
|
|
2019
|
15.8
|
1077
|
37724
|
|
2018
|
16.6
|
1023
|
37330
|
|
2017
|
16.8
|
954
|
37956
|
|
2016
|
16.1
|
930
|
38078
|
|
2015
|
17.8
|
888
|
36875
|
|
2014
|
18.8
|
840
|
36153
|
|
2013
|
19.2
|
776
|
34735
|
|
2012
|
20.4
|
710
|
35421
|
|
2011
|
19.8
|
652
|
36240
|
|
2010
|
20.3
|
586
|
37689
|
|
2009
|
21.0
|
543
|
36420
|
|
2008
|
21.1
|
531
|
38670
|
|
2007
|
20.9
|
502
|
37397
|
|
2006
|
22.0
|
476
|
36621
|
|
2005
|
23.9
|
457
|
35461
|
|
2004
|
24.6
|
439
|
34037
|
|
2003
|
26.0
|
424
|
33635
|
|
2002
|
25.9
|
414
|
32733
|
|
2001
|
26.9
|
412
|
30341
|
Source: ONS (2023)
(10 marks)
Question 3
What is segment AB depicting in Figure 2? Explain the diagram using an example.
Figure 2
(10 marks)
Question 4
A producer has the following problem:
According to producer theory, what variables would get the producer to increase the demand for labour? What variables are missing from the theory? Explain. (10 marks)
Section B - Answer two questions
600 words per question
Question 5
Alex has an Instagram account and is keen to become an ‘influencer’ . Alex has noticed that they will get one new follower each time they post two pictures of a cat and three pictures of food. It takes Alex 30 minutes to find and take a picture of a cat and 20 minutes to order and take a picture of their food.
Unfortunately, Alex tends to be quite busy during an average week. They sleep nine hours a day, work for 50 hours a week and find that other activities (such as actually eating and travelling) take up around 47 hours a week. Alex can spend the remaining time trying to get as many new followers on Instagram per week as they can.
(a) What is Alex’s utility function? Explain. Draw a set of indifference curves for Alex. (4 marks)
(b) What is Alex’s budget constraint? Explain. Draw this on your diagram for (a). (6 marks)
(c) What is the optimal number of new followers that Alex can get in a week? Explain and show your calculations. (8 marks)
(d) Alex is unhappy about the number of new followers that they can get per week. Using what you know about demand functions in this situation, what can Alex do to increase the number of followers per week? What factors that are not part of the demand function could Alex use to get more followers per week? Explain. (12 marks)
Question 6
Eli owns a social media site that is worth £44 million. There is a 25% chance that the value of shares will become worth £20 million. Eli is hoping to convince an insurance company to provide cover at a fair rate of £0.25 per £1 of cover. Eli’s utility function is u = w 1/2
(a) Prove that at a ‘fair rate’, Eli will purchase full insurance coverage. (8 marks)
(b) Sketch the utility of wealth diagram for Eli with wealth on the x-axis and utility on the y-axis. Ensure that you indicate the total cost of the insurance to Eli and the maximum amount that Eli would be willing to pay for the insurance. (8 marks)
(c) If the insurance premium is YK , where K is the coverage, then a fair rate of insurance is when Y = π , where π is the probability of the insurance company having to pay out. Show what would happen to Eli’s optimal insurance coverage if the insurance company opted to charge a rate of Y above the fair rate. (6 marks)
(d) Do you think that an insurance company would provide full cover at the fair rate? Explain. (8 marks)
Question 7
Tim’s Coffee shop is planning to produce and sell 300000 coffees in 2023. Tim’s Coffee Shop’s production function is:
f(L, K) = 40L0.8 K 0.2 ,
Where L and K are the inputs of labour and capital, respectively. Tim’s Coffee Shop’s fixed cost of production is £10000. Wages per hour are £20 and rent per hour is £10. Tim’s Coffee Shop has a fixed cost of £10000.
(a) Find Tim’s Coffee Shop’s total cost function. (8 marks)
(b) Tim’s Coffee Shop has a rival who has the following total cost function:
TC = 1000 + 10Q2 + Q.
(i) What is the rival coffee shop’s short run supply curve if fixed costs are sunk? (6 marks)
(ii) The rival coffee shop makes a total revenue of £2000. What should they do in the long run? (6 marks)
(c) Many coffee shops have been closing due to the ‘cost of living’ crisis. Explain the decisions that these coffee shops are making using producer (cost) theory. Does the theory need any additions to help explain the phenomenon we casually observe?
Explain. (10 marks)