Virtually all countries face the question of how best to distribute benefits to citizens in
need of assistance. One common way to distribute food is by using vouchers that can
only be used to purchase food, but no non-food items (such as, e.g., tobacco or alcohol).
Another way to distribute benefits is through cash assistance. Both the US and the UK
have a system in place that combines cash transfers with vouchers (see, e.g., Wikipedia
on Electronic Benefit Transfer, or the discussion in the Guardian on a switch of local
councils in the UK towards food vouchers, here. This question investigates the effects of
different methods of supporting (or taxing) consumption.
Mr. Jones currently receives a cash benefit of £1, 000 per month, which he allocates only
to food (F) and housing (H). Food currently costs £10 per “unit” (think, e.g., of a “unit”
as the cost of a shopping trip, but consider food a homogeneous and perfectly divisible
good for this question). This benefit is Mr. Jones’ only source of income.
Housing costs vary directly with the quality and size of an apartment. Mr. Jones currently
spends £600 per month to rent a 600 square foot apartment. Housing currently is priced
as £1 per square foot, with a maximum square footage in Mr. Jones’ local area of 1, 000.
You can assume that Mr. Jones’ preferences satisfy all five axioms that we discussed in
the lectures, and that his subsistence needs are satisfied by all relevant bundles.
(a) Derive Mr. Jones’ budget constraint (resource constraint and budget line), denoting
“housing” as the dependent variable. Illustrate his budget constraint and his current
consumption bun ndle. Explain your diagram carefully. (10 points)
(b) Now assume that the government introduces a “bedroom tax”.1 Any apartment that
is smaller than 400 square feet will not incur this tax. However, for apartments of
more than 400 square feet, there will be a tax per square foot of £1 on any footage
above 400. I.e., the housing cost of every square foot above 400 will effectively
increase to £2 per square foot. Is it possible that this bedroom tax could force Mr.
Jones to reduce the amount of food he purchases? Is it certain that he reduces the
amount of food he buys? Discuss your answer making use of economic theory and
diagrams. (15 points)
(c) Consider Mr. Jones’ situation without the bedroom tax (as in part (a)). Due to a
particularly good harvest, food prices have decreased such that Mr. Jones will only
have to spend £8 per “unit” of food. At the same time, because the government
wants to decrease its deficit, it cuts cash benefits to £800 per month. Illustrate the
change in Mr. Jones’ choice problem. Discuss the following, making use of utility
theory: Will Mr. Jones continue to live in the same apartment? Will he reduce his
food shopping? Is he better or worse off after the change? (10 points)
(d) Consider again the case of food costing £8 per unit and no bedroom tax. However,
instead of the proposed cut in cash benefits of part (c), the government now
proposes the following scheme: Cash benefits will be cut to £600 per month, but
food vouchers will be introduced that allow 40 units of food to be bought per month
(irrespective or market prices). Illustrate the effect of this proposal on Mr. Jones’
budget constraint and compare it to the reduction in cash benefits proposed in part
(c) and his original constraint in part (a). Under which benefit system, the one in
(c) or the one in (d), is Mr. Jones better off? Explain. (15 points)
2. Fiscal vs. monetary policy.
A closed economy with a fixed price level is characterised by the following relationships:
C = 50 + 0.8Y
I = 150 − 10r (2)
G = 250 (3)
t = 0.25 (4)
= 0.5Y − 20r (5)
Ms = 400 (6)
where C is consumption, I is investment, G is government spending, t is the tax rate,
is demand for real money balances, Ms
is money supply, Y
is disposable income,
Y is national income (=output), and r is the interest rate (given in per cent). The price
level is fixed at P = 1.
(a) Derive equilibrium national income and interest rate, and illustrate the equilibrium
in a diagram. (8 point (b) Because of an increase in pessimism of consumers, the consumption function changes
and becomes C = 0.8Y
. Suppose the government wants to keep output/national
income at the same level it had before this wave of pessimism. The government
wants to achieve this by either increasing government expenditure, or through a
decrease in the tax rate. Derive the necessary values of G or t that will achieve this.
Discuss which of these policies might be preferred by the government, and why.
(c) With the consumption function as in (b) above and the fiscal policy as in (a), would
monetary policy be an effective alternative to fiscal policy to keep output/national
income at its level of part (a)? Discuss. (7 points)
(d) Now assume that with the consumption function of part (b), the government wants
to increase equilibrium output to 1, 200. It considers two alternative policies: (i)
Increase G and keep both monetary policy and t fixed at their levels of part (a), (ii)
keep fiscal policy at its level of part (a) and instead use monetary policy. Which
policy is more likely to be effective? Discuss. (5 points)
3. Statements about Economic Theory.
The following are four statements that relate to the material we discussed during the
course. They aim to test the depth of your understanding of common concepts. For
each of these statements, state whether they are TRUE, FALSE or UNCERTAIN and
provide a brief explanation (based on economic theory / diagrams / analytical derivations,
as appropriate) for why they are TRUE/FALSE/UNCERTAIN. Your mark will depend
entirely on your explanation. I.e., you will not encounter a single answer that only states
TRUE, FALSE, or UNCERTAIN when you submit your test.
(a) When the equilibrium price of a good in a market falls, consumer surplus in that
market rises. (5 points)
(b) It is possible for all goods to be luxury goods. (5 points)
(c) If nominal interest rates hit a value of zero, monetary policy becomes ineffective.
(d) If the central bank raises the required reserve ratio, the money supply will fall. (5