Practice Test 1 - Math for business | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố HCM

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Môn: Math for business

Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

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Profile Mai Nguyệt
26/10/2020 MATH FOR BUSINESS
REVIEW MID-TERM 2 SEM 1-2020-2021
REVIEW FOR MID-TERM
Exercise 1: Assume that for a good, fixed costs are 84 and variable costs per unit are Q + 2, and
the demand function is
2 50P Q
. Find the value of output which the firm
a) Break-evens
b) Make a loss of 324 units
c) Maximum profit.
Exercise 2: Saving/loans
2.1. Thomas saves $500 000 in a bank account. Afterwards, $50 000 is additionally invested in the
acoount at the beginning of each subsequent year from then. He expects to withdraw all the saving
amount to buy a new car in next 5 years. The interest rate is 7% compounded annually. How much
money will Thomas receive at that time?
2.2. A person borrows $100 000 at the beginning of a year and agrees to repay the loan in ten equal
instalments at the end of each year. Interest is charged at a rate of 6% compounded annually. Find
the annual repayment.
Exercise 3: The price series of a good at the end of the years from 2017 to 2019 is given as follows:
$2 500 $3 000 $3 600, , . The inflation rate in 2018 and 2019 are 2% and 3% respectively.
a) Find the real house price of each year adjusted to prices prevailing at the
end of 2018.
b) If the index number of 2020 is 115 which is given 2018 as base year. The nominal price of good
in that year is $ Work out the inflation rate of 2020. 3 700.
Exercise 4: As the graph is shown below about the supply curve of a good.
S
26/10/2020 MATH FOR BUSINESS
REVIEW MID-TERM 2 SEM 1-2020-2021
a) Find the slope of the supply curve and deduce the corresponding supply function.
b) Sketch the graph of the demand fuction
2 50
D
P Q
. What are the equilibrium price and
quantity?
c) Suppose the government decides to impose a tax t per unit. What are the equilibrium price and
quantity with tax? Given market clearing (equilibrium), find the value of t maximizing the
government's total tax revenue in term of t. Total tax revenue is the product of tax per unit and
the amount of goods or services sold.
Exercise 5: Given the demand function
500 3 2 0.01
A
Q P P Y
Q
where
20, 30 5000
A
P P and Y
. Find
a) The price elasticity of demand.
b) The cross-price elasticity of demand.
c) The income elasticity of demand. Whether a good is normal or inferior good?
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26/10/2020 MATH FOR BUSINESS REVIEW FOR MID-TERM
Exercise 1: Assume that for a good, fixed costs are 84 and variable costs per unit are Q + 2, and
the demand function is P  2Q  50 . Find the value of output which the firm a) Break-evens b) Make a loss of 324 units c) Maximum profit.
Exercise 2: Saving/loans
2.1. Thomas saves $500 000 in a bank account. Afterwards, $50 000 is additionally invested in the
acoount at the beginning of each subsequent year from then. He expects to withdraw all the saving
amount to buy a new car in next 5 years. The interest rate is 7% compounded annually. How much
money will Thomas receive at that time?
2.2. A person borrows $100 000 at the beginning of a year and agrees to repay the loan in ten equal
instalments at the end of each year. Interest is charged at a rate of 6% compounded annually. Find the annual repayment.
Exercise 3: The price series of a good at the end of the years from 2017 to 2019 is given as follows: $2 500 $3 000 , $3 600 ,
. The inflation rate in 2018 and 2019 are 2% and 3% respectively.
a) Find the real house price of each year adjusted to prices prevailing at the end of 2018.
b) If the index number of 2020 is 115 which is given 2018 as base year. The nominal price of good in that year is $
Work out the inflation rate of 2020. 3 700.
Exercise 4: As the graph is shown below about the supply curve of a good. S REVIEW MID-TERM 2 SEM 1-2020-2021 26/10/2020 MATH FOR BUSINESS
a) Find the slope of the supply curve and deduce the corresponding supply function.
b) Sketch the graph of the demand fuction P  2
Q  50. What are the equilibrium price and D quantity?
c) Suppose the government decides to impose a tax t per unit. What are the equilibrium price and
quantity with tax? Given market clearing (equilibrium), find the value of t maximizing the
government's total tax revenue in term of t. Total tax revenue is the product of tax per unit and
the amount of goods or services sold.
Exercise 5: Given the demand function Q  500 3P 2P 0.01Y Q A
where P  20, P 30 and Y  5000. Find A
a) The price elasticity of demand.
b) The cross-price elasticity of demand.
c) The income elasticity of demand. Whether a good is normal or inferior good? REVIEW MID-TERM 2 SEM 1-2020-2021