Question 1
In a income model, are income, consumption, government expenditure, investment, exports and imports respectively. The income model is
(a) Let
where is disposable income and is taxation, and are the autonomous taxation and autonomous import respectively. Let , leaving three parameters, , the autonomous taxation, , the propensity to consume and , the propensity to import, as free parameters, with . Derive an expression for the equilibrium level of income, in terms of .
3 marks
(b) Obtain an expression for , and assess briefly the effect of the difference in the propensities, , on the equilibrium income, .
7 marks
(10 marks)
Question 2
Assume the following market model
(a) Calculate the equilibrium price and quantity first without tax and then with a tax of £5 per unit sold.
3 marks
(b) What proportion of tax is paid by the consumer and what revenue the government raises from tax?
2 marks
(5 marks)
Section B
Question 3
A firm faces a demand curve and the total cost given by
(a) Find the profit-maximizing level of output and price as a function of a tax per unit, .
20 marks
(b) Calculate the effect of changes in on the optimal level of output and price by calculating the two derivatives and interpret the results.
10 marks
(30 marks)
Question 4
(a) Two pollution sources can be cleaned up if money is spent on them according to the functions
where and are the pollution levels from the two sources, and are expenditure levels (in £000s) on pollution reduction. What is the cheapest way (minimum cost) of fixing the total pollution level to 1000?
25 marks
(b) Estimate the change in the minimum cost if the total pollution level is required by law to fall to 950?
5 marks
(30 marks)
Question 5
For the demand function
(a) Calculate revenue and marginal revenue for .
10 marks
(b) Calculate the change in revenue when rises from to .
5 marks
(c) Calculate the consumer surplus for .
10 marks
(25 marks)
