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Dba 103: Introduction To Microeconomics Question Paper
Dba 103: Introduction To Microeconomics
Course:Bachelor Of Commerce
Institution: University Of Nairobi question papers
Exam Year:2013
UNIVERSITY OF NAIROBI
FIRST SEMESTER EXAMINATION- 2012/2013
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF COMMERCE
DBA 103: INTRODUCTION TO MICRO ECONOMICS
DATE : JANUARY 30, 2013 TIME: 9.00AM-11.00AM
INSTRUCTIONS:
There are FIVE questions on this paper. Answer any THREE questions.
QUESTION ONE.
Suppose that an individual has three uses of his time: sleeping, working and consuming goods. Let
S= hours of sleep, L= hours of work C= hours of consumption
Consumption of course is costly so assume that consumption costs 10 cents per minute and consequently the cost of consumption= 6/= = C=60x10xC= 600C
Now suppose that an individual receives utility from sleeping and consumption given by a utility function
U (S, C) = S0.25 C0.75
Finally assume that the individual’s entire income comes from working and that for his work,the individual receives 400/= per hour.
If this person has to maximize utility, how many hours should he spend sleeping, working and consuming?
More generally explain why this is really a problem in choosing between “goods’ S an C
What is the budget constraint of these two goods? That is, what are the opportunity costs of S and C, and how much “income” does this person have to devote to them?
What kind of utility function does this person have? Using the results of this type of function, calculate his demand functions for S and C as functions of prices and income described in part (c) above?
QUESTION TWO
The demand function of a commodity is described by the exponential function
P = 10.5e-0.1Q
Where Q is the quantity demanded and TR = Total revenue.
Determine;
The quantity for which the tatal revenue is maximized.
The maximum revenue.
( Hint: revenue is maximized when dTR/dQ=0 )
In making a certain item, a business firm has discovered that the demand function for the item is represented by
P = 50/(vx)
The cost function of producing X items is given by
C = 0.5X + 500
Find the price per unit that yields a maximum profit (p^*)
Find the output level that maximizes profit (p^*)
Find the maximum profit (p^*)
Show the second-order-condition (S.O.C) has been fulfilled.
QUESTION THREE
If th production function of a product Q depends on capital (K) and labour (L) hired according to the Cobb-Douglas production function.
Q = 10K1/2L1/2
And cost of capital and labour is given by V and W respectively so that
TC = VK = WL
If the producer wishes rto produce 40 units of the product.
Show the relevant cost minimization problem using the Langragian expression.
From a) above, derive the total cost function.
If W = V = 4, calculate the total cost (min, max) of producing the 40 units of the product.
QUESTION FOUR
A firm produces amount X and Y of two different grades of bread using the same production process. The production possibility curve (PPC), showing th maximum output of either good attainable for any given level of output of the other is given as
X2 + 2X = 10 – Y
What are the largest amounts of X and Y that can be produced?
What amounts of X and Y must be produced to have:
0.25Y = X
Y = 2X
QUESTION FIVE
Given the demand and supply functions shown below, calculate the equilibrium price and quantity at which the markets clear (Qe and Pe)
Qd = 90 – 2P
Qs = vP-3
A monopolist sells two products X and Yand has the following demand functions for each of the products.
0.1Px – 1.2 = 0.2X = 0
10Py – 32 – 4y = 0
His joint cost function s given to be
TC – X2 – 2XY – Y2 = 0
Find the price and the output level of each good that will maximize profits. (p^*)
Using the second order condition (S.O.C) show that profits have a maximum at this point.
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