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EC1060 Introduction to Quantitative Economics
Creation date：2024-05-08 17:55:43
Belonging category：经济Economics
Tag EC1060
Introduction to Quantitative Economics

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EC1060

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)

EC1060

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)






EC1060

3 (Question 5 continued overleaf)

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)
Case category
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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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