Practice Test 2 - 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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Review midterm M4B
1
SAMPLE MIDTERM TEST
Duration: 90 minutes
Question 1:
Given that the supply graph passing through (0;8) and (10;18) while the demand
graph passing through (20;20) and (10;50).
a) Find the supply and demand function.
b) Roughly sketch the graphs of both the demand function and the
supply function on the same plane on A4 paper. What are the xy-
equilibrium price and quantity without tax?
c) The government decides to impose a tax t per unit. What are the
new equilibrium price and quantity?
d) Find the value of t which maximises the government’s total tax revenue on the
assumption that equilibrium conditions prevail in the market.
Question 2:
The table below shows government expenditure (in billions of dollars) on education
for four consecutive years, together with the rate of inflation for each year.
2004
2005
2006
2007
Spending
236
240
267
276
Inflation rate
4.7
4.2
3.4
a) Find the values of expenditure at constant 2004 prices and hence calculate the
index numbers of real government expenditure.
b) If the index number of the real data in 2003 is 95.6 and the nominal spending is
$225, find the rate of inflation for 2004. Give your answer correct to 1 decimal
place.
Question 3
3.1. A person invests $5000 at the beginning of a year in a savings account that
offers a return of 9% compounded semi-annually. At the beginning of every
Review midterm M4B
2
subsequent six-month period, an additional $1000 is invested in the account. How
much will there be in the account at the end of ten years?
3.2. Determine the monthly repayments needed to repay a $100 000 loan which is
paid back over 25 years when the interest rate is 8% compounded annually.
Question 4:
Find an expression for the profit function given the demand function
2Ā + ÿ = 25
and the average cost function
�㔴�㔶
=
32
Ā
+ 5
a) Show an expression for the profit in term of Q
b) Find the values of Q for which the firm
i. breaks even
ii. maximizes profit. What is the value of maximum profit?
Question 5:
Given the demand function
Ā = 1000 2 5ÿ 2 2ÿ
�㔴
2
+ 0.005�㕌
3
where P = 15, P = 20 and Y = 100, find
A
(a) the price elasticity of demand
(b) the cross-price elasticity of demand. Is the alternative good substitutable or
complementary?
(c) the income elasticity of demand.
Give your answer correct to 2 decimal places.
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Review midterm M4B SAMPLE MIDTERM TEST Duration: 90 minutes Question 1:
Given that the supply graph passing through (0;8) and (10;18) while the demand
graph passing through (20;20) and (10;50).
a) Find the supply and demand function.
b) Roughly sketch the graphs of both the demand function and the
supply function on the same xy-plane on A4 paper. What are the
equilibrium price and quantity without tax?
c) The government decides to impose a tax t per unit. What are the
new equilibrium price and quantity?
d) Find the value of t which maximises the government’s total tax revenue on the
assumption that equilibrium conditions prevail in the market. Question 2:
The table below shows government expenditure (in billions of dollars) on education
for four consecutive years, together with the rate of inflation for each year. 2004 2005 2006 2007 Spending 236 240 267 276 Inflation rate 4.7 4.2 3.4
a) Find the values of expenditure at constant 2004 prices and hence calculate the
index numbers of real government expenditure.
b) If the index number of the real data in 2003 is 95.6 and the nominal spending is
$225, find the rate of inflation for 2004. Give your answer correct to 1 decimal place. Question 3
3.1. A person invests $5000 at the beginning of a year in a savings account that
offers a return of 9% compounded semi-annually. At the beginning of every 1 Review midterm M4B
subsequent six-month period, an additional $1000 is invested in the account. How
much will there be in the account at the end of ten years?
3.2. Determine the monthly repayments needed to repay a $100 000 loan which is
paid back over 25 years when the interest rate is 8% compounded annually. Question 4:
Find an expression for the profit function given the demand function 2Ā + ÿ = 25 and the average cost function 32 �㔴�㔶 = + 5 Ā
a) Show an expression for the profit in term of Q
b) Find the values of Q for which the firm i. breaks even
ii. maximizes profit. What is the value of maximum profit? Question 5: Given the demand function Ā = 1000 2 5ÿ 2 2ÿ 2 �㔴 + 0.005�㕌3
where P = 15, PA = 20 and Y = 100, find
(a) the price elasticity of demand
(b) the cross-price elasticity of demand. Is the alternative good substitutable or complementary?
(c) the income elasticity of demand.
Give your answer correct to 2 decimal places. 2