**MAASAI MARA UNIVERSITY**

**REGULAR UNIVERSITY EXAMINATIONS**

**2016/2017 ACADEMIC YEAR**

**FIRST YEAR, SECOND SEMESTER**

**SCHOOL OF BUSINESS A ND ECONOMICS **

**BSc. AGRICULTURAL ECONOMICS AND RESOURCE MANAGEMENT, BSc. AGRIBUSINESS MANAGEMENT, BSc. ECONOMICS, BSc. FINANCIAL ECONOMICS, BSc. ECONOMICS AND STATISTICS**

**COURSE CODE: ECO 1204**

**COURSE TITLE: MATHEMATICS FOR ECONOMISTS I**

**DATE: 8TH MAY 2017 TIME: 0830-1030 HRS**

**INSTRUCTIONS TO CANDIDATES**

**Answer Question ONE and any other THREE questions**

**This paper consists of 3 printed pages. Please turn over.**

**Question One**

a. Distinguish between the following economic concepts as used in Mathematics for Economists

i. Composite function and Behavioral equation

ii. LM and IS curves

iii. Disjoint sets and Symmetric matrix (6 Marks)

b. What are the advantages of Mathematics for Economists over literary Economics (6 Marks)

c. Given :

Compute the equilibrium level of income and Consumption (7 Marks)

d. Briefly discuss the conditions for non-singularity of a matrix (3 Marks)

e. Given

**Question Two**

a. What are the limitations of Static (equilibrium) Analysis (4 Marks)

b. Given the demand and supply functions for 2 commodities as follows:

Calculate the equilibrium prices and quantities of the two commodities (5 Marks)

c. Highlight the properties of Determinants in Matrices (6 Marks)

**Question Three**

The economy of country X has three sectors: Agriculture, Industry and Service. Each unit of gross output of Agricultural product (QA) requires inputs of 0.3 units of its own product, 0.4 units of Industrial product and 0.2 units of Service sector products. Each unit of gross output of Industrial product (QI) requires 0.2 units of its own product, 0.1 units of Agricultural products and 0.5 units of Service sector products. Each unit of gross output of Service product (Qs) requires 0.2 units of its own product, 0.3 units of Agricultural products and 0.4 units of Industrial product.

a. What is the general use of the input- output analysis (2 Marks)

b. What are the assumptions of the input-output model (3 Marks)

c. Using Leontief Inverse Rule, find the required gross outputs QA, QI and Qs when the final demands for Agriculture, Industry and Service sector products are given as 400, 600 and 200 respectively (10 Marks)

**Question Four**

Kenya’s economy is defined by the following model:

a. Explain the meaning of the following parameters and variable in the Consumption and Tax functions: C0, C1, Yd , t0 and t1 (5 Marks)

b. Find the County’s equilibrium Income (Y*) and Consumption (C*) (10 Marks)

**Question Five**

a. Consider the following system of three equations:

x + y – 2z = 4

2x + 2y +3z =15

x +3y + 2z = 12

Using matrix inversion method, determine the values of x, y and z (8 Marks)

b. Find the homogeneity of the following function

c. Compute f[h(x)] given h(x) = (15 – x2) (3 marks)