Maths set of exercises spring 2010

Set of problemsMaths for Economics and Business

Vilnius-Kaunas (Lithuania) 2009/2010

MATHEMATICS

FOR ECONOMICS AND BUSINESS

SET OF EXERCISES

Spring Semester 2010

Lecturer P_ U_E_ R _T _A _S, J. M_I_Q_U_E_L.

THE following set of problems is based on the book Ian Jacques “Mathematics for Economics and Business” (5th Edition) Prentice Hall.

The set of problems has to be hand in to the Lecturer by 15th of June (by mail) or in a hard copy to the Academic Department. If you hand in the set of problems, that is optional, you can get till 2 extra points that will be added to the mark obtained at the final exam.

The completion of the set of exercises is optional but it may help the students to improve their marks.

EVALUATION CRITERIA :

A) 0.5 points if the student hand in the exercises before the dead-.line. If the student hand in the exercises after the dead-line he/she will not get any additional point.

B) 1.5 points if there are not important mistakes in the answers.0.75 points if there are some important mistakes in the answers.0.25 points if there are many important mistakes.0 points if the student doesn’t hand in the exercises before or after the dead-line.

I wish you good luck!!(1)Picture: “2+2 is 5” taken in Kaunas (on a wall besides “Blues & Orange” Baras ) in Kaunas old town.. Lithuania. September 2009.

1rst. Exercise: Check section 2.1 Quadratic functions.

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Use “the formula” to solve the following quadratic equations (Round your answers to 2 decimal places).The “formula” to solve quadratic equations is

a)

b)

c)

d)

e)

2ond. Exercise: Check Section 2.1: Quadratic functions. Page 126

Given the supply and demand functions

+18 +14

8 +120

calculate the equilibrium price and quantity

3rd. Exercise: Check section 4.3: Marginal function.

If the production function is

Where Q denotes output and L denotes the size of the workforce, calculate the value of MPL (marginal product of labour) when

a) L=1b) L=10c) L=100d) L=2000

4th. Exercise: Check section 2.2 Revenue cost and profit.

If fixed costs are 6, variable costs per unit are 2 and demand function is

Obtain an expression of ∏ (profit) in terms of Q and hence sketch a graph of ∏ against Q.

a) For what values 0f Q does the firm break even?

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b) What is the maximum profit?

5th Exercise: Check Section 4.2: Rules of differentiation

Differentiate

a)

b)

c)

d)

e)

f)

6 th. Exercise: Check the section 7. Basic matrix operations Page 465-467

Let

Find (where possible)

a) ABb) BAc) CDd) DCe) ACf) CA

7 th. Exercise: Check section 7.2: Matrix inversion (page 475)

The equilibrium price P1 and P2 for two goods satisfy the equations

Express this system in matrix form and hence find the values of and

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8th exercise: Check section 5.6: Lagrange multipliers. Page 412

Use Lagrange multipliers to find the optimal value of

Subject to the constraint

9 th. Exercise: Check section 7.3: Cramer’s rule. Page 493

Solve the system of equations

=

Using Cramer’s rule to find

10th Exercise: Check section 5.2: Partial elasticity and marginal functions. Page 360.

Given the utility functionDetermine the value of the marginal utilities

and When =300. Hence estimate the change in utility when decreases from 200 to 199 and increases from 300 to 301.

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Technology

Maths set of exercises spring 2010