Applied Quantitative Methods for Business in China

1. The daily supply and demand for 15 ml cups of coffee at Amenities Building can be expressed by the

following equations (where is the price in pence per cup and and are the supplied and demanded quantities in
cups):
(Supply) (Demand)
(a) [10%] Solve for the equilibrium quantity and price
(b) [15%] The government decides to discourage the drinking of coffee by adding a 30%
value-added-tax. Define the new supply function and calculate the new equilibrium
quantity and price .
(c) [10%] Sketch the Demand function and both Supply functions (with P on the vertical
axis) stating the slopes and the values where these functions cross the vertical axis. On the same graph,
using the answers in (a) and (b), label the equilibrium values for ,
, , and .
(d) [10%] Explain how the market gets to the new equilibrium.
2. Determine how long it will take for a sum of money to triple in value if invested at an interest rate of
3% compounded
?(a) annually (b) monthly Determine the AER in (a) – (c).
(c) continuously.
Turn Over
1
[15%]
3. A small business has a choice of spending £4 000 today on one of the two projects. The revenue flows from
the two projects during the next three years are listed in the following table. If the interest rate is 15%
compounded annually, which of these two projects would you advise the company to invest in? Using the
appropriate methods to appraise the two projects.
??????Revenue (£)
??End of year
1 2 3
Project A
3 000 2 000 1 000
Project B
500 1 000 5 000
????????????4. Matthew plans to buy a car which costs £20 000. He does not have savings so has to borrow
money from the bank. The bank’s interest rate is 7.5% compounded monthly. His monthly salary is £1500 and he
has a budget of £350 for the car’s monthly repayment. Suppose the monthly repayment is made at the end of
each month and Matthew has to repay the loan over 5 years. Can Matthew afford this car?

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