Elementary Mathematical Techniques for Economics
Instructor: Ram Sewak Dubey ECON 317: Problem Set 1 September 18, 2018
1. [Basic Algebra-I]
(a) A person buys q1, q2, q3 and q4 units of four goods whose prices per unit are, re- spectively, $1, $2, $3 and $4. What is the total expenditure? What will be the total expenditure if the prices change to $4, $3, $2 and $1 per unit respectively?
(b) A rental car costs $20 per day in fixed charges and $ 0.75 per mile. How much must the consumer pay for the month of September 2018 when she drives x miles per day during the month.
(c) A company has fixed costs of 50000 dollars per year and variable costs of 50 dollars per unit produced. Find an expression for the total cost per unit (total average cost) incurred by the company if it produces 1000 units in one year. What is the average variable cost incurred by the company?
(d) A person has an annual salary of $ 60000 and then receives a raise of 5% followed by a further increase of 10%. What is the person’s new yearly salary? What will be the new salary if she receives a raise of 10% followed by a further increase of 5%. How do the two answers compare? Explain.
2. [Basic Algebra - II]
(a) Prove that
a + a · p 100
− ( a + a·p100
) · p
100 can be written as
a [
1 − ( p
100
)2] .
(b) An item initially costs $200 and then its price is lowered by 10%. Afterwards the price is increased by 10%. What is the final price?
(c) An item initially costs $a and then its price is lowered by p%. Afterwards the (new) price is increased by p%. What is the final price? After solving this problem, look at the expression in part (a).
(d) What is the result if one first increases the price by p% and then lowers the (new) price by p%
3. [Basic Algebra- III]
Which of the following equations are functions and why?
Submission deadline: 11:59pm, September 26, 2018 Page 1 of 3
Instructor: Ram Sewak Dubey ECON 317: Problem Set 1 September 18, 2018
(a) y = −5x + 10,
(b) (2y)2 = x,
(c) y = 25x2,
(d) y = −5x2 + 10x + 25,
(e) x2
36 +
y2
64 = 1,
(f) x = 10.
4. [Basic Algebra- IV]
Solve the following equations for the variables specified.
(a)
x = 1 3 (y − 3)+ 3y, for y.
(b) −ax + b = cx + d, for x.
(c) KL
1 2 = Y0, for L.
(d) px + qy = n, for y.
(e) 1 r + a 1 r − b
= c, for r.
Submission deadline: 11:59pm, September 26, 2018 Page 2 of 3
Instructor: Ram Sewak Dubey ECON 317: Problem Set 1 September 18, 2018
(f) Y = a(Y − tY − k)+ b + I0 + G + cY, for Y.
5. [Basic Algebra- V]
Solve the following pair of simultaneous equations for x and y.
ax +(1 − b)y = C
and
bx +(1 − a)y = D.
Submission deadline: 11:59pm, September 26, 2018 Page 3 of 3