Quatitive Methods Samples
PROBLEMS
1. The market for opera tickets can be described by the following demand and supply curves:
QD = 20000 – 90P QS = 10000 + 110P
i) What is the equilibrium price and quantity in the ticket market? ii) Suppose that the Government imposes a price ceiling of £25 on opera tickets. How many tickets are now sold in the market? Does this get more or less people to attend the opera.
2. The market for pizza can be described by the following demand and supply curves:
QD = 300 – 20P QS = 20P - 100
i) What is the equilibrium price and quantity in the pizza market? ii) Suppose that the price of hamburgers, a substitute for pizza, doubles. This leads to a doubling in demand for pizza. What is the new equilibrium price and quantity in the pizza market? iii) Given the initial demand and supply equations suppose now that the Government imposes a tax of £3 per pizza. What is the new equilibrium price and quantity in the pizza market?
3. A firm has two possible production processes for a new product. For process A, the fixed costs per month are £20000 and the unit variable costs are £5. For process B, the fixed costs per month are £10000 and the unit variable costs £9
(a) Find the level of output for which total costs are the same for the two processes. (b) If the selling price is £15 per unit, find the break- even point for each process. c) Sketch a graph of the two cost equations on the same pair of axes and advise the firm as to when they should use A and when they should use B.
4. A company wishes to hire a piece of machinery and estimates that it will be required for at least 7 days. It has a choice of two firms, A and B, from which to hire. Firm A makes an initial charge of £100 and subsequently £15 per day. Firm B makes no initial charge but charges £25 per day.
(a) Find the number of days’ hire for which
1. The market for opera tickets can be described by the following demand and supply curves:
QD = 20000 – 90P QS = 10000 + 110P
i) What is the equilibrium price and quantity in the ticket market? ii) Suppose that the Government imposes a price ceiling of £25 on opera tickets. How many tickets are now sold in the market? Does this get more or less people to attend the opera.
2. The market for pizza can be described by the following demand and supply curves:
QD = 300 – 20P QS = 20P - 100
i) What is the equilibrium price and quantity in the pizza market? ii) Suppose that the price of hamburgers, a substitute for pizza, doubles. This leads to a doubling in demand for pizza. What is the new equilibrium price and quantity in the pizza market? iii) Given the initial demand and supply equations suppose now that the Government imposes a tax of £3 per pizza. What is the new equilibrium price and quantity in the pizza market?
3. A firm has two possible production processes for a new product. For process A, the fixed costs per month are £20000 and the unit variable costs are £5. For process B, the fixed costs per month are £10000 and the unit variable costs £9
(a) Find the level of output for which total costs are the same for the two processes. (b) If the selling price is £15 per unit, find the break- even point for each process. c) Sketch a graph of the two cost equations on the same pair of axes and advise the firm as to when they should use A and when they should use B.
4. A company wishes to hire a piece of machinery and estimates that it will be required for at least 7 days. It has a choice of two firms, A and B, from which to hire. Firm A makes an initial charge of £100 and subsequently £15 per day. Firm B makes no initial charge but charges £25 per day.
(a) Find the number of days’ hire for which