# Essay about Supply and Demand and Optimal Consumption Bundle

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UNIVERSITY COLLEGE LONDON

EXAMINATION FOR INTERNAL STUDENTS

MODULE CODE

ECON1604

ASSESSMENT
PATTERN

ECON1604B

MODULE NAME

Economics 1 (Combined Studies)

DATE

22-May-09

TIME

14:30

TIME ALLOWED

3 Hours 0 Minutes

2008/09-ECON 16048-001-EXAM-147

University College London

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ECONOMICS 1604: ECONOMICS 1
Please answer ALL questions in Section A from Sections Band

C (25%

(50%)

and ONE question EACH

each). All answers should be accompanied by

a brief explanation or discussion. Correct but unexplained answers will not receive high marks.
In cases where a student answers more questions than requested by the exam­ ination 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.

Section A. Answer ALL questions, .
Al

Suppose that the demand function for a good is QD(P) lOO-p and its supply function Qs(p) = p, where p is the price of the good in £/unit.
Find the equilibrium price and quantity consumed. At the equilibrium point, what are the price elasticities of demand and supply, € and .", respectively? Use the formula � = � to determine the impact of a
£l/unit specific tax, T, on the equilibrium price paid by the consumer,
PD. Verify the magnitude of the increase in the equilibrium price paid by the consumer by calculating the new equilibrium directly with a shifted inverse supply curve.

A2

You like to consume coffee and sugar, C and S , respectively, in an a: b ratio, i.e., you always want to have � �. Express your utility function as a function of C and S, U(C, S). If you are given prices Pc and Ps (in
£/unit) for coffee and sugar, respectively, along with your income, m
(in f), then what is your optimal consumption bundle, (C', S'), and maximised level of utility, U(C', S')?

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consumer has the utility function U(X, Y) = X1/4y3/4 and faces prices px = py = 1 (in £/unit). Suppose that. she is given an en­ dowment of the two goods, (wx, wy) = (50,50). What is this con­ sumer's optimal consumption bundle, (X', y.)? If px
2 instead, ceteris paribus, then what is the new optimal consumption bundle,
(X", Y")? If the consumer has an exogenous income of m = 100 (in
£) rather than an endowment, then what is her new optimal consump­ tion bundle, (X', yl) when px
2, ceteris paribus? Discuss why the reduction in consumption of good X due to the price increase is less when income is endogenous.

A3 A

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ECON1604

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A4

A firm manufactures output, q, according to the production function f(L, K) = L'/2 Kl/2, where L and K indicate the input of labour and capital, respectively. Find the optimal amount of each input to use and the resulting cost function, C(q), given the wage rate, w = 1 (in
£/unit labour), and rental rate, r = 1 (in £/unit capital). Using the
Lagrange multiplier, determine the increase in the minimised cost if the production target, q, is increased by one unit. Verify your answer by differentiating the cost function, C(q), to obtain the marginal cost.

A5

What are the four conditions for price-taking behaviour in an industry?
Explain which one may be weakened as a result of marketing.

A6

The Federal Reserve has recently reported that the Ml money mul­ tiplier has dropped substantially over the past few months and even fallen slightly below unity. Define the money multiplier and provide some possible reasons for this sudden change.

A7

Derive a model of frictional unemployment for an economy based on unemployed workers finding jobs at a rate f and employed workers losing their jobs at some rate s (assume that the labour force is con­ stant). Explain how such a model leads to the Beveridge curve - an inverse relationship between the number of vacancies created and the
unemployment…