Get premium membership and access revision papers, questions with answers as well as video lessons.
Got a question or eager to learn? Discover limitless learning on WhatsApp now -
Start Now!
Econ 230: Mathematics For Economists 1 Question Paper
Econ 230: Mathematics For Economists 1
Course:Bachelor Of Science In Economics And Statistics
Institution: Chuka University question papers
Exam Year:2010
CHUKA UNIVERSITY
COLLEGE
UNIVERSITY EXAMINATIONS
SECOND YEAR EXAMINATION FOR THE AWARD OF DEGREE OF BACHELOR OF SCIENCE (ECONOMICS & STATISTICS)
ECON 230: MATHEMATICS FOR ECONOMISTS 1
STREAM: B.SC.(ECON & STATISTICS) Y2S1 TIME: 2 HOURS
DAY/DATE: TUESDAY 27/7/2010 11.30 A.M. – 1.30 P.M.
INSTRUCTIONS
Answer question One and any other two questions.
Do not write on the question paper.
1. (a) Explain the importance of mathematical economics. [5 marks]
(b) Verify the distributive law, given A={4, 5), B = {3,6,7} and C = {2, 3}.
[4 marks]
(c) Find the equilibrium price and quantity for the market model with hyperbolic demand function and quadratic supply function.
[3 marks]
(d) Evaluate the following
[3 marks]
(e) The demand and supply functions of a two commodity market model are as follows:
Qd1 = 10 – 2P1 + P2
Qs1 = -2 + 3P1
Qd2 = 15 + P1 – P2
Qs2 = -1 + 2P2
Find equilibrium price and quantity. [4 marks]
(f) Consider the following national income model
Y = C + I + G
C = a + bYd
T = tY
G = Go
(i) Calculate the equilibrium income [2 marks]
(ii) Find the following multipliers and interpret your results
(a) Government expenditure multiplier [1 mark]
(b) Investment multiplier [1 mark]
(c) Income tax rate multiplier [1 mark]
(g) Two farmers (P and Q) sold the following amounts of wheat and barley to the National Cereals Board (NCB).
Farmer
Sales in Tons
Wheat
Barley
Farmer P
20
40
Farmer Q
30
50
The farmers made Kshs 500 profit per ton from wheat and Ksh 700 per ton from barley.
(i) How much wheat did Q sell to NCB? [1 mark]
(ii) How much barley did P sell to NCB? [1 mark]
(iii) What is the total amount of barley sold to NCB by both farmers?
[1 mark]
(iv) Using matrix multiplier, find the profits made by each of the farmers from both wheat and barley. [3 marks]
2. (a) You are given the following information
Y = C + I + G
C = 100 + 0.8Yd
T = 10 + 0.1 Y
I = 50
G = 30
(i) Find and. [6 marks]
(b) A firm has a budget of B = 180 for purchasing K and L priced KSh.3 and Ksh.4 per unit, respectively
(i) Find the corresponding isocost line. [1 mark]
(ii) Sketch the line on the Cartesian coordinate plane. [1 mark]
(iii) (a) If the budget line declines by 40 percent, find the new
isocost line. [1 mark]
(b) Sketch the new and the new isocost lines on the same
Cartesian Coordinate graph. [1 mark]
(iv) (a) If Pk rises to 6, find the new isocost line. [1 mark]
(b) Sketch the current isocost line and the original one.
[1 mark]
(c) (i) A firm has a fixed cost of 5 and its variable costs per unit
are 3.
Find the firm’s total cost function. [1 mark]
(ii) You are given the following total cost function:
Find:
(a) The fixed costs (FC) [1 mark]
(b) The variable costs (VC) [1 mark]
(c) The Average Variable costs (AVC) [1 mark]
(d) A production possibility frontier (PPF) is given by the following function:
P = 36 – 2Q
(i) Sketch the PPF [1 mark]
(ii) How much of the product P will be produced if all the resources
are devoted to the production of that product? [1 mark]
(iii) Is the combination of (P, Q) = (8, 16) feasible? Comment on your
answer. [2 marks]
Q.3 (i) Find the following limit
[3 marks]
(ii) Determine whether the following function is continous at the specified
point.
at [7 marks]
(iii) (a) Find the MPL and MPK for the following production function.
Q = AKL [2 marks]
(b) Express MPL in terms of ,Q and L and MPK in terms of
, Q and K. [4 marks]
(iv) Find the marginal utility for the following bivariate utility function
U = 15x?y? [4 marks]
Q.4 (a) Consider the following national income model
Y = C + I +G
C = Co + C1Y
I = io + i1Y
G = 1000
(i) What are the endogenous and exogenous variables and parameters
in the model? [3 marks]
(ii) Express the model in matrix form. [2 marks]
(b) A three sector input-output table is given by the following:
1
2
3
D
X
1
X11
X12
X13
D1
X1
2
X21
X22
X23
D2
X2
3
X31
X32
X33
D3
X3
V
V1
V2
V3
X
X1
X2
X3
(i) If the input-output coefficients are denoted by ij (i, j = 1,2,3),
write out these input-output coefficients in term so Xij (i,j = 1,2,3) and the total outputs. [3 marks]
(ii) Find X12, X31, X33 in terms of ij and Xj. [3 marks]
(iii) Find the GNP by expenditure approach. [2 marks]
(iv) Derive the input-output model. [7 marks]
---------------------------------------------------------------------------------------------
More Question Papers
Popular Exams
Return to Question Papers