# ECO 113 INTRODUCTION TO MATHS I Click to view MAASAI MARA UNIVERSITY

REGULAR UNIVERSITY EXAMINATIONS
FIRST YEAR SECOND SEMESTER

BACHELOR OF ECONOMICS

COURSE CODE: ECO 113
COURSE TITLE: INTRODUCTION TO MATHS I

DATE: 11TH MAY 2016 TIME: 11-1 PM
INSTRUCTIONS TO CANDIDATES
Answer Question ONE and any other THREE questions

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

QUESTION ONE( 25 MARKS)
An economy has three industries, government (G), Agriculture (A) and manufacturing (M). The input output table for three industries is given as: Calculate the total output required for each industry when the final demand changes to 300,350 and 450 for government, agriculture and manufacturing respectively ( 15 marks)
Evaluate by means of integration by substitution:
(5 marks)
Given the following equation Calculate
The cross price elasticity of demand. What is the relationship between good x and good y. Explain. (3 marks)
The income elasticity of demand (2 marks)

QUESTION TWO ( 15 MARKS)
The demand function of a product is given as:
(p+10)(q+20)=1000

The supply function is given as:
q-4p+10=0
Determine the equilibrium price and quantity (6 marks)
Determine the producer surplus under market equilibrium (6 marks)
State and explain the types of returns to scale (3 marks)

QUESTION THREE ( 15 MARKS)
Given the utility function(x+2)(y+1) and P_x=4,P_y=6 and income of the consumer=130
Write the consumer’s optimization problem (2 marks)
Find the optimal level of x and y. (7 marks)
Prove Euler’s theorem using the following function
Q=96K^0.3 L^0.7 (6 marks)

QUESTION FOUR ( 15 MARKS)
Let the national income model be given as QUESTION FIVE ( 15 MARKS)
Find the rank of the matrix (Visited 37 times, 1 visits today) 