Ollscoil na hÉireann, Gaillimh

GX_____

National University of Ireland, Galway

Semester 1 Examinations 2008/2009

Exam Code(s)

2BA5

Exam(s)

2nd B.A. (Economic & Social Studies)

Module Code(s)

EC222

Module(s)

Techniques of Analysis

Paper No.

1

Repeat Paper

External Examiner(s)

Professor Robert Wright

Internal Examiner(s)

Professor Eamon O’Shea

Mr. Stephen McNena

Instructions:

There are two sections in this exam. Please answer any 6

questions from section A and 6 questions from section B.

Duration

3 hours

No. of Pages

6 pages, including this cover sheet

Department(s)

Economics

Course Co-ordinator(s)

Breda Lally, St. Angela’s College, Sligo

Requirements:

MCQ

No

Handout

Handout of formulae to be distributed at St. Angela’s

College, Sligo

Statistical Tables

Yes, to be distributed at St. Angela’s College, Sligo

Graph Paper

Yes, if students request it

Log Graph Paper

No

Other Material

No

SECTION A MATHS

Answer any 6 of the 8 questions. 15 minutes per question.

1. (a) Consider the demand function represented by the equation: Qd = 50 – 5P

(i) Express Total Revenue (TR) as a function of Qd.

(ii) What is the slope of the demand curve? What is the value of its intercept?

(iii) Sketch the demand curve.

(iv) At P = 6, calculate the quantity and the total revenue.

(b) Consider the following production function: Y = A f (K, L) = 10AK0.5L0.5

where Y is national output, A is technological knowledge, K is the capital stock,

and L is labour.

Transform this Cobb-Douglas production function into a linear model using

logarithms.

2. (a) A firm that makes paint sells their product for €7. Their cost function is

represented by the equation: TC = 200 + 5Q.

(i) Calculate the breakeven quantity.

(ii) Determine the Total Revenue, Fixed Cost, Variable Cost and Total Costs.

(iii) Sketch the Total Cost and Total Revenue curves.

(b) Consider the following demand and supply equations:

Demand: P = 100 – 3Q

Supply: P = 10 + 2Q

(i) Solve for the equilibrium price and quantity.

(ii) What are the slopes of the two curves?

3. Consider an open economy described by the following equations:

C = 300 + 0.9Yd Govt spending = 600

I (autonomous) = 400 Tax rate = 20% of incomes

Exports = 800 Imports = 27.5% of disposable income

Note that C, Y and M are endogenous, and I, G, t and X are exogenous constants.

(a) Solve for the equilibrium national income, Y.

(b) Then calculate disposable income, consumption and imports.

(c) Determine the Marginal Propensity to Consume and the Marginal Propensity to

Save.

(d) Calculate the expenditure multiplier.

(e) If an injection of extra autonomous expenditure causes national income to rise by

400, calculate the size of the extra expenditure.

4. Consider the demand function represented by the equation:

Qd = 30 - ⅓ P

(a) Express Total Revenue (TR) as a function of Q.

(b) Determine the equation for Marginal Revenue.

(c) Using differentiation, calculate the quantity where TR is maximised.

(d) Calculate the price where TR is maximised.

(e) Calculate the maximum Total Revenue.

5. Assume a Total Cost function of the form: TC = 30Q - 15Q² + 3Q3

(a) Derive a function for Average Cost (AC).

(b) Derive a function for Marginal Cost (MC).

(c) Find the levels of output that minimise AC and MC.

(d) Calculate the minimum AC and the minimum MC.

(e) Using algebra, confirm that AC = MC when AC is at a minimum.

6. A firm faces the following demand and Total Cost functions:

P = 125 – Q

TC = 500 + 5Q + 0.5Q²

(a) Determine the equations for Total Revenue, Marginal Revenue, Average Cost,

Marginal Cost and Profit.

(b) Derive the profit-maximising level of output.

(c) Calculate the maximum profit.

(d) Derive the price and Marginal Revenue at this level of output.

7. A monopolist produces a single good (X) but sells it in two separate markets. The

cost function is TC = 120 + 8Q. The demand function in each market is

P1 = 50 – 4q1 P2 = 80 – 3q2

where P1 and q1, P2 and q2 are the prices and quantity in markets 1 and 2. Find the

prices and quantities in each market that maximise overall profits.

8. A firm has a Cobb-Douglas production function as follows: Q = L0.3K0.7

The price of labour is 3 and the price of capital is 15. The firm faces a total cost

constraint of 150.

Determine the values of L and K for which production is maximised, subject to the

cost constraint.

SECTION B STATISTICS

Answer any 6 of the 8 questions. 15 minutes per question.

1. (a) Your sell newspapers at €1.80 each, breakfast rolls at €3.50 each and textbooks

at €40 per book. During one day you sell 150 newspapers, 25 breakfast rolls and 10

textbooks. What is the weighted mean selling price?

(b) You invest some of your savings in a managed fund. The annual percentage

returns earned by the fund for the last 5 years are outlined in the table below.

Calculate the geometric mean annual return earned by the fund.

9.4% 13.8% 1.7% 11.9% 4.7%

(c) (i) Calculate the mean, median and mode of the following set of numbers.

0, 9, 9, 6, 9, 7, 9, 3, 3, 2, 1

(ii) Explain carefully why the median is sometimes a preferable measure of central

location than the mean.

2. (a) A student is taking two courses: maths and economics. The probability the

student will pass maths is 0.75, and the probability of passing economics is 0.90.

The probability of passing both subjects is 0.70. What is the probability of passing at

least one subject?

(b) A firm uses two types of machines, the S40 and the S60. The probability of the

S40 machine being available is 0.90 and the probability of the S60 being available

is 0.80. What is the probability that both types of machine are available? What is

the probability that both types of machine are not available?

(c) If you ask three strangers on campus, what is the probability that:

(i) All were born on a Wednesday?

(ii) All were born on different days of the week?

(d) Sarah is the owner of a convenience store. Sarah collects data on how many items

each customer purchases, as shown in the table below:

X = no. of items

P(x)

0

1

2

3

0.10

0.40

0.30

0.20

(i) Compute the mean and standard deviation for the distribution of number of items.

(ii) If a customer enters the shop, what is the chance that they buy at least 2 items?