THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF ECONOMICS ECON1202/2291 QUANTITATIVE MEHODS A FINAL EXAMINATION SESSION 2 2008
TIME ALLOWED - 3 HOURS

THIS PAPER IS WORTH 60% OF THE TOTAL SUBJECT MARK
Questions: 7 Students must attempt no more than 6 questions Marks per question: 10 Exam weighting: 60%.

Instructions to Students:

- Complete all of the details required on the front page of the examination booklet. - Make sure that you note the SIX(6) questions attempted on the front of your examination booklet - If Seven questions are attempted, the first SIX(6) will be marked. - You may use a non-programmable calculator - Graph paper will be provided. - Answers are to be written in ink. Pencils are permitted for graphing purposes. - The …show more content…

(6 marks) b) Find the price elasticity of demand of the function:

q= At the point where P = 12

1600 − p2 ;

What does the figure you got for elasticity say about the demand for this product? (4 marks)

6

Question 7:
a) Crazy Rugs own 100 glorious Persian rugs which must be sold in the next two periods (period 1 and period 2). Buyers in each period will pay for their purchases at the end of the period. The undiscounted profit functions for sales in period one and two are given by:

π(q1 ) = 50q1 − 0.5(q1 )2 π(q1 ) = 50q2 − 0.5(q2 )2

(7) (8)

Using the method of lagrange calculate the quantities that should be sold in each period supposing that profits are discounted at a rate of 25% per period. (6 marks) b) A mining company must consider between two strategies for mining its resource. By investing $10 million now, it can make a net profit earned at a constant rate of $3 Million per year for 10 years, at which time the resource will be exhausted. Alternatively, the company can invest $15 Million now to obtain a net profit of $5 Million per year for 7 years. Assuming a nominal discount rate of 10% compounding continuously, which gives the highest NPV for the exploitation of the resource. SHOW your WORKING. (4 marks)