You will be given five minutes at the end of the examination to complete the front of any answer books used. May/June 2016 EC /6 A 001

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1 On admission to the examination room, you should acquaint yourself with the instructions below. You must listen carefully to all instructions given by the invigilators. You may read the question paper, but must not write anything until the invigilator informs you that you may start the examination. You will be given five minutes at the end of the examination to complete the front of any answer books used. May/June 2016 A4 Graph Paper Approved calculators permitted Dictionaries are not permitted UNIVERSITY OF READING INTRODUCTORY MATHEMATICS FOR ECONOMICS 1 (EC116) Two hours Answer ALL questions in Section A; and answer TWO questions in Section B.

2 Page 2 SECTION A Answer ALL questions 1. A backpacker budgets 198 per month for hostels and excursions. Hostels cost 6 per night (sometimes the backpacker sleeps on the bus or with friends) and excursions cost 18 each. (a) Obtain an expression for the backpacker s budget constraint and draw the budget line. (b) If the backpacker plans to spend 30 nights in hostels, how many excursions can he or she afford? (c) How many nights of free accommodation are needed for the backpacker to be able to afford one extra excursion? 2. (a) Transpose the following formula to express Y in terms of I. Y = a Y + b + I (b) A consumption function is given by C = a Y + b. It is known that when Y = 10 the value of C is 28 and that when Y = 30 the value of C is 44. (i) By solving a pair of simultaneous equations, find the values of a and b, and deduce that the corresponding savings function is given by S = 0.2Y 20. (6 marks) (ii) Find the equilibrium level of income when planned investment I = 13.

3 Page 3 3. (a) Find the turning point of the function: f 2 x 18 8x x (b) Find the solutions of the equation: x x 0 (c) Draw a sketch of the function in part a), showing all important points. 4. Differentiate: 3 (a) y x 7x 2x 10 2 (b) y 2 x 3 x (c) y 1 3x 7 Turn over

4 Page 4 SECTION B Answer TWO questions 5. A firm faces a demand function given by: P = Q and has the total cost function: TC = Q 12Q Q 3 (a) Show at what output profit is maximised, and the price and the maximum value of profit. (b) What is the effect on profit maximum if taxation is imposed as: (i) A lump sum tax of 120; (ii) A per unit sales tax of 24.

5 Page 5 6. (a) Simplify h 2 h (b) Solve for x: e x (c) The population of a small town was 753 in If the population grows according to the equation 0.03t P 753e where P is the number of persons in the population at time t: i. Graph the population for t = 0 (in 1980) to t = 30 (in 2010) using intervals of t = 5 and from the graph estimate the population in 1990 and ii. Confirm your answers algebraically. (1 mark) iii. In what year will the population reach 1750 persons? (1 mark) Turn over

6 Page 6 7. A manufacturing company faces the following demand curve: q d 190 5p The firm s accountants believe that the supply curve is given by: q s 3p 10 where p denotes price in and q d and q s are quantities demanded and supplied, respectively. (a) Determine the equilibrium price and quantity in the market for the firm. (b) The government now decides to impose a tax of 2 per unit on the quantity supplied and the producer adjusts the supply function to include the tax. Calculate the new market price, and compare the publisher s revenue, after the tax has been paid, to what it was before the tax was imposed. (c) Calculate the government s tax revenue. 8. (a) A box with a lid has a square base of side x cm and height h cm. If the total surface area is 2040 cm 2 write down a formula for the volume V cm 3 and eliminate h to show that V = 510x ½ x 3. (b) Hence find the dimensions giving the maximum possible volume and calculate this volume. (6 marks) (End of Question Paper)