Question 1

On the 1st April 2022, the UK energy price cap increased (on average) from £1,277 to £1,971 per year. Explain and illustrate a method to evaluate the impact that the  price change will have on the average individual. (10 marks)

Question 2

Table 1: Petrol Prices, Road Traffic and Income in the UK and Great Britain

Source:  www.gov.uk (2022)

Table 1 contains information about petrol prices, road traffic and disposable income taken from the ONS. Use consumer theory to explain the changes in car use in the UK. (10 marks)

Question 3

Describe a situation which is best modelled by using quasi-linear preferences. (10 marks)

Question 4

In a budget constraint with endowments, why does the budget line pivot around the endowment point when there is a price change?  Explain and illustrate.(10 marks)

Section B – Answer two questions

600 words per question

Question 5

(a) A researcher has collected data regarding the consumption of two goods in Table 2.

Table 2: Consumption of Good X and Y

(i) Use the data to plot three indifference curves. What type of preferences are represented here? Give an example of Good X and an example of Good Y. (6 marks)

(ii) Give an example utility function and demand functions to represent these goods. (4 marks)

(b) The researcher conducts some interviews regarding Goods X and Y. One of the interviews is with Vic. They find that Vic has the following utility function:

U = 9X0.3 Y 0.7 ,

where X is Vic’s consumption of Good X and Y is Vic’s consumption of Good Y. Use a Lagrangian to derive Vic’s demand function for good X and good Y. (10 marks)

(c) The researcher is producing a statistical report on the relationships between the following variables:

(i) The price of good X and the quantity demanded of good X; (ii) The price of good Y and the quantity demanded of good Y; (iii) The price of good X and the quantity demanded of good Y; (iv) The price good Y and the quantity demanded of good X;    (v) Income and the quantity demanded of good X;                    (vi) Income and quantity demanded of good Y.

Given your answers to (a) and (b), what kind of relationships would you expect the researcher to find? Do you think the researcher should look for any other               relationships? Explain. (10 marks)

Question 6

Bob has the following utility function:

U = F 0.9 E0. 1

where F    is the number of fish consumed and E    is the number of eggs consumed.

(a) The price of fish is £9 and the price of eggs is £8. Bob has a weekly income of £200. Use a Lagrangian to find the optimal amounts of fish and eggs that Bob      consumes in a week. (10 marks)

(b) The price of eggs now rises to £10.

(i) What is the new optimal amount of fish and eggs that Bob consumes each week? (2 marks)

(ii) Calculate the income and substitution effects of the price rise. Draw a diagram of the price rise and show the income and substitution effects. (8 marks)

c) Explain how income and substitution effects are used to classify goods into normal, inferior and Giffen goods. (10 marks)