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```SUMMER TERM 2015
ECON1604: Economics 1 (Combined Studies)
TIME ALLOWANCE: 3 hours
Answer ALL questions from Part A, one from Part B and one from Part C. All answers should be
accompanied by a brief explanation or discussion. Correct but unexplained answers will not receive
high marks.
Questions in Part A carry five per cent of the total mark each and questions in Part B and Part C
carry twenty-five per cent of the total mark each.
In cases where a student answers more questions than requested by the examination rubric, the policy
of the Economics Department is that the student’s first set of answers up to the required number will
be the ones that count (not the best answers). All remaining answers will be ignored.
PART A
Answer ALL questions from this section.
A1 Suppose that the supply function for Utopia’s medical services is QS (p) = p, where p is the price
of medical services in £ per unit. If citizens’ demand for medical services is QC
D (p) = 100 − p,
then what are the equilibrium price and quantity demanded by citizens only? If the demand
function of foreigners living in Utopia is QFD (p) = 120 − 2p, then what is Utopia’s total demand
function, QD (p), for medical services? Factoring in the demand of foreigners, what are the
overall equilibrium price and quantity demanded for medical services in Utopia?
1
1
A2 Your utility function for bagels and coffee is U (B, C) = B 2 C 2 , where B and C denote the
number of bagels and cups of coffee consumed, respectively. Suppose that the price per bagel
and cup of coffee is pB = 1 (in £/bagel) and pC = 1 (in £/cup). Given an exogenous income of
m = 100 (in £), what are your optimal consumption bundle and maximised level of utility? If
the price of bagels increases to p0B = 2, then what are the new optimal consumption bundle and
maximised level of utility?
∂x
∂x
x
A3 The Slutsky equation with an exogenous income is ∂p
= ∂h
∂px − x ∂m , where x and hx are
x
Marshallian and Hicksian demands, respectively, px is the price of the good, and m is the
x
exogenous income. What is the sign of ∂h
∂px ? If the good is normal, then what happens to its
quantity demanded as its own price decreases, ceteris paribus? Now, suppose that income is
endogenous, which means that the Slutsky equation is adjusted to account for the endowment
dx
∂x
x
of good x, ωx , as follows: dp
= ∂h
∂px + (ωx − x) ∂m . For a normal good, does the endowment
x
effect reinforce or oppose the income effect? Explain your answer intuitively by using a diagram
that decomposes the substitution, income, and endowment effects.
ECON1604
1
TURN OVER
A4 An ambitious educational institution, UCL, uses the production function f (L, K) = min{aL L, aK K}
to yield output, where L and K indicate units of lecturers and Kool-Aid used, respectively. What
is the interpretation of the parameters aL and aK ? If the corresponding input prices for lecturers and Kool-Aid are w and r (both in £ per unit of input), respectively, then what is UCL’s
long-run cost, C(q), to produce q units of output? Express your result for C(q) in terms of aL ,
aK , w, r, and q.
A5 Suppose that the industry inverse supply and demand functions for a particular good are pS (Q) =
Q and pD (Q) = 10 − Q, respectively, where Q is the quantity supplied or demanded. What is
the deadweight loss associated with a £4 per unit price ceiling imposed by the government?
A6 Draw a balance sheet for a central bank and put the following items correctly under either
assets or liabilities: (i) government bonds, (ii) domestic coins and notes in circulation; (iii)
foreign currency held by the central bank. Give an example of one asset and one liability on a
commercial bank’s balance sheet.
A7 “Cutting taxes will undoubtedly increase economic (fixed) investment in the economy.” Using
the IS-LM model, illustrate a tax cut in the short run and explain why this statement may not
necessarily be true.
A8 Oil prices fell significantly during the latter half of 2014. Assuming that a lower oil price is
maintained in the medium run, illustrate using AS-AD and IS-LM diagrams the impact of a
sharp fall in oil price on the world (i.e. a closed) economy. Show what happens to price level,
output, interest rate, consumption and investment in both the short and medium run. You may
assume that the world economy was in medium run equilibrium before the price drop. In one
sentence, give an important reason why some countries do better than others when the oil price
falls sharply.
A9 Write down the Phillips curve relationship between inflation, expected inflation and unemployment and define the sacrifice ratio for a disinflationary policy. Suppose the central bank of an
economy with high inflation is seeking your advice on the best way to reduce its inflation rate
to a much lower level. If the economy’s labour market is characterised by wage agreements
staggered over time across the majority of employment sectors, in which wage levels are fixed
for long periods, what specific recommendations would you make to the central bank?
A10 You are given that, in year t, the 1-year domestic nominal interest rate is it , the 1-year foreign
nominal interest rate is i∗t and the nominal exchange rate between domestic and foreign currency
is Et . Derive the interest parity condition and comment on any assumptions you have made
about investors’ behaviour. Use this relation to explain why an announcement by the Bank of
England’s governor in June 2014 that he plans to raise interest rates in the future led immediately
to an appreciation of the pound against the US dollar.
ECON1604
2
CONTINUED
PART B
Answer ONE question from this section.
1
3
B1 A consumer can buy two goods, X and Y . Her utility function is U (X, Y ) = X 4 Y 4 . The prices
of the two goods are pX = 1 and pY = 1 (both in £ per unit), and her exogenous income is
m = 100 (in £).
(a) Solve the consumer’s utility-maximisation problem to obtain the optimal consumption bundle and maximised utility level.
(b) Repeat part (a) with a different price p0X = 2.
(c) What should be this consumer’s adjusted income, m0 , so that her original optimal consumption bundle from part (a) is just affordable under the prices given in part (b)? What will
be the consumer’s maximised level of utility with adjusted income m0 and prices p0X = 2
and pY = 1?
(d) How much minimum extra income should be given to the consumer under prices p0X = 2
and pY = 1 so that her maximised utility is equal to that in part (a)?
(e) What kinds of income adjustments are offered in parts (c) and (d)? Which one of the
two is a true cost-of-living adjustment (COLA)? Discuss why consumer price index (CPI)
adjustments may be preferrable to use in practice, e.g. by governments.
ECON1604
3
TURN OVER
B2 The industry inverse demand curve for a particular good is pD (Q) = 24 − Q, where Q is the
industry-wide quantity demanded or supplied. There are four identical firms in this perfectly
competitive industry, each with cost function C(q) = 9 + q 2 , where q is each firm’s output and
Q = 4q.
(a) Determine each firm’s average cost, average variable cost, and marginal cost functions.
Prove that the marginal cost curve passes through the minimum point of the average cost
curve.
(b) If p denotes the output price per unit, then what is each firm’s short-run supply curve in
terms of p? What is the industry short-run supply curve in terms of p?
(c) What are the equilibrium price and quantity for this industry? How much profit is earned
by each firm?
(d) Based on the profit earned, is there any incentive for firms to enter or to exit this industry
in the long run? Explain your answer by referring to the result from part (c).
(e) What is the maximum amount that these four firms would be willing to pay as a bribe to
the regulator in order to permit them to act as a monopoly? Note that the formation of a
monopoly would increase the total producer surplus to the detriment of consumers. What
will be the deadweight loss from having a monopoly relative to the perfectly competitive
equilibrium in part (c)?
ECON1604
4
CONTINUED
PART C
Answer ONE question from this section.
C1 Suppose you are asked to model unemployment in an economy with search frictions. Unemployed
workers move into jobs at a rate f , which depends on the number of job vacancies (v), a job
search effectiveness parameter (i), and an index of skills mismatch (mm). Assume further that
employed workers lose their jobs at a rate s and that the labour force L is, for the moment,
constant.
(a) Obtain an expression for the evolution of the unemployment rate u over time. Derive from
this the steady-state unemployment rate and describe how the relationship between the
unemployment rate and the number of vacancies leads to the Beveridge Curve.
(b) Explain how the unemployment rate determines the number of vacancies created through
the labour market (the job creation curve).
(c) Suggest two possible factors that may cause the Beveridge curve to shift leftwards (inwards)
(d) What would be the impact on unemployment and vacancies of a rise in the minimum wage?
Show the results graphically along with a brief explanation in words.
(e) Suppose now that a booming economy requires skilled workers from abroad and that these
workers increase the labour force at a rate α. In other words, assume that dL
dt = αL and
that all new individuals enter the economy as employed. If the labour force growth rate
α = 1%, the job separation rate s = 1% and the job finding rate f = 8%, obtain a new
expression and the resulting value for the steady-state unemployment rate. Using your
model explain what effect even stronger labour force growth of this type would have on the
ECON1604
5
TURN OVER
C2 Consider the Mundell-Fleming model for a small open economy with floating or fixed exchange
rates:
IS:
Y = C(Y − T ) + I(Y, i) + G −
LM:
M = P Y L(i),
IRP:
i = i∗ .
IM (Y, )
+ X(Y ∗ , ),
Here, for the domestic economy, C is the consumption function, Y is domestic (real) GDP, T
is government taxes, I is investment, G is government spending, IM is imports, X is exports,
M is the nominal money stock, P is the domestic price level and L(i) is the liquidity function.
The domestic and foreign interest rates are i and i∗ respectively and Y ∗ is foreign (real) GDP.
The real exchange rate is given by and you may assume that price levels remain constant
throughout.
(a) Using the IS equation, show how private saving and investment are related to the budget
and trade deficits. What are the possible consequences on these factors for an open economy
wishing to increase government spending without raising taxes?
(b) Show graphically and in words the effect on domestic output, consumption, investment and
net exports of a sharp reduction in government spending G (i) under floating exchange
rates and (ii) under fixed exchange rates.
(c) State the Marshall-Lerner condition and any necessary assumptions for it to be valid.
Explain why a sudden depreciation in the domestic currency might lead to a worsening of