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1 (Question 2 continued overleaf)
UNIVERSITY OF WARWICK

Summer Examinations 2020/21

Introduction to Quantitative Economics


Time Allowed: 2 Hours.

Read all instructions carefully – and read through the entire paper at least once before you
start entering your answers.

There are TWO Sections in this paper. Answer ALL THREE questions in Section A (50 marks
total) and ALL THREE questions in Section B (50 marks total).

Approved pocket calculators are allowed.

You should not submit answers to more than the required number of questions. If you do,
we will mark the questions in the order that they appear, up to the required number of
questions in each section.


Section A: Answer ALL THREE questions


1. Sherry is on vacation and wants to bring souvenirs home to family and friends. Her
souvenir budget is $100, and she can choose between T-shirts, which cost $20 for each
pack, and key chains, which cost $5 for each pack. Sherry’s utility function is defined
as = //; where is one pack of T-shirts and is one pack of key chains.

(a) Draw Sherry's budget line and indifference curve. (5 marks)

(b) What is the slope of Sherry's budget line? What is the slope of the utility function?
Interpret the slope of the utility function. (5 marks)

(c) What is Sherry’s utility maximising combination of and ? (5 marks)


2. A monopolist faces a market demand curve given by:

= 70 − .

(a) If the monopolist can produce at constant average and marginal costs of = =
6, what output level will the monopolist choose to maximise profits? What is the
price at this output level? What are the monopolist’s profits? (5 marks)

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2 (Continued overleaf)

(b) Assume instead that the monopolist has a cost structure where total costs are
described by:
() = 0.25 − 5 + 300

With the monopolist facing the same market demand and marginal revenue, what
price–quantity combination will be chosen now to maximise profits? What will the
profits be? (5 marks)

(c) Assume now that a third cost structure explains the monopolist’s position, with
total costs given by:
() = 0.0133 − 5 + 250

Again, calculate the monopolist’s price–quantity combination that maximises
profits. What will profit be? Hint: Set = as usual and use the quadratic
formula to solve the second-order equation for Q. (5 marks)


3.
(a) Why does an ‘external social cost’ lead to inefficient overproduction? (7 marks)

(b) The table below provides information about the marginal social cost and marginal
social benefit of streetlights, which are a public good.

Quantity
(streetlights per
block)
Marginal social
benefit
(dollars per year)
Marginal social
cost
(dollars per year)
0 0 0
1 14 4
2 12 7
3 10 10
4 8 13
5 6 16
6 4 19

(i) What is the number of streetlights per block that a private company would
provide? Why? (7 marks)
(ii) What is the efficient quantity? (6 marks)






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Section B: Answer ALL THREE questions.


4. The following table presents the price and aggregate quantity of some goods in an
economy in 2016 and 2019. A, B, and C are the products of this economy, but A is not a
final good. Products D and E are imported final goods from abroad. Calculate:

Good 2016 2019
Quantity Price Quantity Price
A 25 1.5 30 1.6
B 50 7.5 60 8
C 40 6 50 7
D 30 5 35 5.5
E 60 2 70 2.5

(a) Inflation through the GDP deflator (2016 is the base year). (4 marks)

(b) Inflation through CPI (2016 is the base year). (4 marks)

(c) Explain briefly demand-pull and cost-push inflation theories. Do you think the
difference between answers in (a) and (b) can be attributed to one of these
theories? Explain (7 marks)


5. A small open economy is described by the following equations:

= 40 + 0.8( − )
= 200 − 15
= 300 − 40

= 2 − 50
= 300, = 300, = 4000, = 4 ∗ = 5

(a) Derive and graph the ∗ and ∗curves. (5 marks)

(b) Find the equilibrium level of , and . (3 marks)









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(c) If the economy follows a floating exchange rate regime and the government
believes that to reduce levels of unemployment, the government expenditure
should increase by 30 units, what happens to the equilibrium level of , , and
the money supply? (Use a fully labelled graph for your discussion and explain the
results of this expansionary fiscal policy) (6 marks)

(d) Answer part (c) again but assume this time the economy follows a fixed exchange
rate regime. (Use a fully labelled graph for your discussion and explain the results)
(6 marks)


6. Assume the central capital accumulation equation in the Solow model can be written in
a dynamic form for the aggregate variables (not per labour), as = + − ,
and also assume labour force grows at rate , this means we have:
= (1 + ).

(a) Write down the above capital accumulation equation in terms of capital per labour
( = ). (Note: The time subscript of the numerator and denominator should not
be different). (5 marks)

(b) From the equation you derived for part (a), write an expression for ∆. How
does it differ from the one obtained for the model without labour population
growth? (Sketch a fully labelled graph showing the new investment per labour and
the new depreciation per labour graphs and the steady state capital per labour)
(5 marks)

(c) Suppose that the labour population growth rate exogenously and permanently
increases to a higher level . What are the effects on output per worker in the long
run? Explain your answer while referring to the general impact of the labour
population growth in the Solow model. (5 marks)