1. Consider the following cobweb model:

Yt l 2Pt
xt= 15-Pt
Yt Xt

Where Yt is the supply of a product, xt the demand and Pt the price at time t. Let the initial price Po 4 at time 0.
Formulate the problem as a difference equation.

(ii) Solve the difference equation with the given information.

2. A simple economy depends on the three commodities; oil, corn and coffee. Production of 1 unit of oil requires 0.2 units of oil, 0.4 units of corn and no units of coffee. To produce 1 unit of coffee requires 0.2 units oil, 1 unit of corn and 0.2 units of coffee.
Find the input-output matrix for this economy. Find the gross production required to meet a demand of 1000 units of oil, corn and coffee each.

3.(a) Find solution of the following differential equation:

y' with =1
Find solution of the following difference equation: Yt 2 l -Yt 4t

4.(a) If A and B are two sets, prove that A U B B U A.
A car dealer has 350 cars with different types of extra features. You will find number of cars with.

Air conditioning 130
Power steering 255
Navigation system 110
Both P and N 75
All three extra features P and N 10
N only (Without either P or A or both) 10
Without any of the extra features mentioned above 20

Determine the number of cars.
having both navigation and air conditioning but no power steering i.e; (NnA)p.

(ii) having only air conditioning i.e., A (NUP).

(iii) having both air conditioning and power steering but no navigation system, i.e, (Anp)N.
having only power steering i.e., P(AUN).

5. Assume that the demand function is given by: 5p^2-190p 1805 and supply function, by 20p^2 -160p 320. Find the equilibrium price and consumer surplus.

6. Find b such that given below is continuous.


2X^2 b if x 1

-x^3 if x -1

7. Differentiate: y sqrt(x)^sqrt(x).e^x

8. <img src='./qimages/9752-8.jpg'> <br><br>


9. Determine the eigen values and eigen vectors of the matrix A is given by

1 2
2 1


10. Use the limit definition to compute the derivative, for 3x 7.

11. Given the matrices: <img src='./qimages/9752-11.jpg'> <br><br>

Find 2A 3B-C.

12. Find the linear approximation using Taylor Series for about x O.