Section A

1.        For parts a, b and c refer to a good for which the supply and demand equations are given by:

= 250 − 15

= 100 + 10

where Qd, Qs and P represent, respectively, the quantity demanded, the quantity supplied in units per week, and the good’s price in £.

Which of the following statements are true, false or uncertain? Fully explain your reasons by drawing a relevant diagram for each part:

a) when P = £10 there is an excess demand of 100 units;

b) when Q = 160 units per week the market is in equilibrium;

c) if the government imposed a fixed tax of £5 per unit produced, the equilibrium quantity will increase while the equilibrium price will fall.

Parts d and e refer to a single-price profit-maximising monopolist whose demand curve and total cost curve are given by:

= −0.5

= 10 + 0.75

where TC is measured in £k per week and Q represents output measured in 1000s of units per week.

d) Show that the price elasticity of demand is constant, for all values of A, and is always equal to –2.

e) What is the profit-maximising output, and the monopolist’s total profit?

Section B

The Wall Street Journal, January 4, 2010, p. R1., reported that Junk bonds had strong returns in 2009. A random sample of 15 junk bonds from this population was collected which contained information (annual return as %) for each junk bond.

a)  Compute  the  mean,  median,  the  first  quartile,  second  quartile,  third  quartile  and interquartile range. Is data symmetric? Explain.

b)  Compute the standard deviation and coefficient of variation.

c)  Compute  and  interpret  the  Pearson  median-based  measure  of  skewness.  Can  we assume that the returns for junk bonds are distributed as a normal random variable? Explain.

d)  Using the empirical rule, what interval contains approximately 95% of the data? Explain.

e)  Based on your answer of (a), (b), (c), what are the appropriate central tendency and dispersion measures to be used to accurately represent the data above, assuming no additional observation is added?

Section C

3.   A firm’s production function is given by = 0. 5 0.25 . The firm is perfectly competitive and hires its machines at a constant rental rate of r = 5 pounds per unit and its workers at a constant wage rate of w = 4 pounds per unit and the firm has a budget of 1200 pounds to produce the given output.

a) Assess whether this function is homogeneous; and, if so, of what degree. What returns to scale does this production function exhibit? Interpret your answer.            (10 marks)

b) Using Lagrange multiplier method, find out the maximum profits subject to the production cost constraint.                                                                                            (20 marks)

c) Suppose that the market wage rate and the rental rate of machines both doubled, what would be the impact on optimal quantities of capital, labour and output compared to your answer in part (b)?                                                                                       (20 marks)

d) If the firm decided to decrease the units of labour by five units, estimate the required increase in capital in order to maintain the same level of output as in part (b). Does the firm still at the optimum output level?                                                            (20 marks)

e) Using your answer to (b), derive the total cost function as a function in Q alone and prove that it is an increasing function.                                                                   (30 marks)

4.   Suppose you have provided with the individual’s utility function = , where X and Y are the quantities of two goods purchased and and are parameters. The monthly income is M pounds and the prices are and pounds per unit of X and Y respectively.

a) Find out the demand function for good X (the expression of the utility-maximising quantity of X that this person will wish to buy) as a function of the parameters and , PX, and M.

(20 marks)

b) Based on your answer in part (b), find the own-price, cross-price and income elasticities of demand for good X and comment on your results.                                      (20 marks)

c) Find out the expressions of goods X and Y that maximise the utility function.  Following on from this, find the values of X and Y assuming that = 0.5, = 1.5, = 2, = 3, and =

200 .                                                                                                              (20 marks)

d) If the consumer decided to decrease the quantity consumed of good X by 9 units, estimate the required increase in good Y in order to maintain the same level of utility satisfaction as in part (c).                                                                                                    (20 marks)

e) Suppose that the price of god y doubled, what would be the optimal quantities of X, Y and total utility? Is the consumer still at the optimum utility level? Support your answer with diagram.                                                                                                       (20 marks)

Section D

5.

a) Table below contains the yields for a money market account and a five-year certificate of deposit (CD) for 25 banks in the United States, as of March 29, 2010.

Bank

Location

Money CD-

Market 5Year

Data extracted from www.bankrate.com.