Econ 503
Student Name :
Mid-Term Exam
Dr. Hamad Al-Sheikh
Student No:
Answer only Five out of the following six questions:
Q1: The following model was used to estimate the monthly car sales in a given region:
Sales=B1+B2 Wages+B3 Treasury Bill Rate + B4 Consumer Price Index
Parameters
Values
Standard Error
T-Stat
B1
4.9
10.7
B2
10.3
1.1
B3
-140.5
57.3
B4
-35.6
10.6
N = 88 ; R2= .89 ; O2e σσσσ= 236 ;
1st)
2nd)
3rd)
Sales are in Millions of Riyals
Explain the results in words?
Explain what the Coefficient of determination means in this case?
Compute the T-statistic and test the hypothesis that B2 is significant against the alternative that it is not?
Q2: A) You have just finished your Master degree from KSU and the local boss of Toyota who heard about your
expertise summoned you to his office. He just received a demand estimation for Toyota sales completed by a
consultant Professor who graduated from unknown American University. The sales forecast is:
Q1=10.1+6.3P1+3.7P2-11.6P3+2.7P4-2.1Y
Where P1 is the price of Toyota , P2 is price of Nisan Cars , P3 is price of Ford Cars , P4 is price of GMC Cars ,
and Y is Income.
The boss was so outraged that he wanted to fire the consultant. You being naturally unselfish, would you back
the decision of the boss and why ? or rather think that he simply should get rid of the consultant and hire you
instead and why ?
B) The cost function for a firm is : C=6L+6K ; output must be equal to 36 units and the production function is :
Q=L.K ; Using Lagrangian multipliers , find out cost minimizing K and L demand and Cost of producing 36
Q3: A consumer has the following utility function:
U = 4 X1 X 2 - 2 X21 –3 X22 ;and his income is Y = 2 X1 + 3 X 2 ; where Y = 200
1st)
2nd)
3rd)
What are the conditions for the consumer optimal allocation mathematically and graphically ?
Set up the lagrangian function for this consumer ?
Find the optimal demand for X1 and X2 and cheek that it is a maximum ?
Q4.
Consider the following short-run production function for Star Inc.
; Where X is the quantity of Input X
Y = 5 X2 - .2 X3
1st.
Determine the MPx and APx functions ?
2nd.
Find X that maximizes Y ?
3rd.
Find value of X at which MPx takes its maximum value ?
4th.
Find value of X at which APx takes its maximum value ?
Q5: Aproduction function :
Q = .5 LK - .10 L2 - .05 K2
The per unit cost of L=SR 2 for K=SR 4. The firm wants to maximize output provided that cost does not exceed
SR 100.
1st.
Formulate the Lagrangian function ?
L ( L,K,  ) = Q -  ( CL L + CK K – C )λ
2nd.
3rd.
Find the optional demand functions for L and K as well as  ?
What is the total output based on your answer in B. ?
Q6: During the last few days the Superior Company has been running into problems with its computer system.
The last run of production cost schedule resulted in the incomplete listing shown below. From your knowledge
of cost theory , fill in the blanks .
Q
TC
TFC
TVC
ATC
AFC
AVC
MC
0
1
2
3
4
5
6
7
8
9
10
40
-----------------------------------------
---------------------------------------------
--------20
--------40
--------96
---------
x
52
----21.33
--------15.67
-----------------
x
-----------------------------------------
x
------------------------10
----15
-----
x
------------4
--------------------45
Q2: The following is the demand function of a book publishing company:
Q=5000-4000 P+0.5 I+1.5 A+0.02 Pop
Where Q is quantity , P is price , I is income , A is advertising expeeenditures and Pop is population.
Determine the demand faced by the publishing firm in a typical market where:
P=10
I=30000
A=10000
Pop=1000000
-
Calculate the price elasticity of demand at the point given above and comment on the nature of demand
for the product of the publishing firm. Based on your results would you advice the firm to increase its price
from 10 to 15 ? Justify your advice.
-
Calculate the income elasticity of demand at the above point and comment on the nature of the product
of the firm.
-
Calculate the advertising elasticity of demand for the firm. Based on your results would you advise the
firm to increase its advertising expenditures from 10000 to 15000 ? Justify your advice.
Q3: The following schedule shows the total product (TP) function in the short-run:
-
If the price of the product is 5 while the price of input is 10.
How many units of X will the firm use in the short-run ?
-
What will the profits of the firm be at the above point ?
-
If the price of input X increases to 15 , what will happen to the above point of optimal factor use ?
Q4: The selling price of a product produced by a certain firm was 2 SR per unit . Fixed costs were 60000 Srand
variable costs were 1 SR per unit . Use this information to fill in the blanks of the following table and to find the
point of break_even EBIT for the firm :
-
Show the situation diagrammatically in an approximate way .
Q4: phoenix Lumber Company uses the number of construction permits issued to help estimate demand (sales)
The firm collected the following data on annual sales and number of construction permits issued in its market
area :
Year
19X1
19X2
19X3
19X4
19X5
19X6
19X7
No.of Construction
permits Issued( 000)
6.50
6.20
6.60
7.30
7.80
8.20
8.30
Sales
(!000000)
10.30
10.10
10.50
10.80
11.20
11.40
11.30
(One) Which variable is the dependent variable and which is the independent variable ?
(Two) Determine the estimated regression Line.
(Three) Test the hypothesis ( at the .05 significance level) that there is no relationship between the variables.
(Four) Calculate the coefficient of determination. Give an economic interpretation to the value obtained.
(Five) Perform an analysis of variance on regression including an F-test (at the .05 significance level) of the
overall significance of the result .
(Six)
Suppose that 8.000 construction permits are expected to be issued in 19X8. What woud be the point
estimate of Phoenix Lumber Company”s sales for 19X8 ?
(NOTE :This problem requires the use of statistical tables.)
Q : Delta Inc. operates in perfect competition market ; the market demand function is :
And the total cost function for the firm is :TC= Q + 0.05 Q2
1st)
P = 50 - 0.02 Q
calculate the price and quantity combination that would maximize profit for this competitive firm ?
What is its profit in this case ?
2nd)
Do the same in A but assume now that the firm is a monopolist ?
3rd)
What is the difference in profit between A and B ?
Q : Star Inc. produces two products ( X1 and X2 ) using two inputs ( labor and capital ). The firm has 160 units
of capital and 24 units of labor.
Producing one unit of X1 requires 5 units of capital and one unit of labor.
Producing one unit of X2 requires 10 units of capital and one unit of labor.
If the profit margin to X1 is 90 SR per unit and for X2 is 100 SR per unit.
1st)
Formulate the L.P of this problem
2nd)
Graph the feasible region for this firm and indicate the Iso-profit line and show its slope ?
3rd)
Find the optimal product mix for this firm and its maximum total net profit ?
Q : You being an excellent student and a promising professional , who is fascinated by learning new things . You
like your managerial economics course to the extent that you talk about how great and useful this course is to
decision markers . One of your friends who is not as quick as you are in learning new ideas wants you to explain
-
what is managerial economics is all about ?
what is rule in decision making ?
how he / she could benefit from studying managerial economics ?
what did you study in your class ( managerial economics )
what did you think of the course ?
Q : Use the graph to answer the following questions :
A) What is the price and output of this monopolist ?
B) What is the size of loss or profit at equilibrium ?
C)What do you expect the elasticity of demand at equilibrium ?
4th)
What is the price and quantity at which demand has unitary elasticity ?
Q : The Zinger Company manufactures and sells a line of sewing machines. Demand per period (Q) for a
particular model is given by the following relationship:
Q = 400 - .5 P
Where P is price. Total costs ( including a “ normal” return to the owners) of producing Q units period are:
TC= 20,000 +50Q+ 3 Q2
(One) Express total profits ( ЛЛ ) in term of Q.
(Two) At what level of output are total profits maximized ? What price will be charged ? What are total profits
at this output level ?
(Three) What model of market pricing has been assumed in this problem ? Justify your answer.
Q: Zar Island Gas Company is the sole producer of natural gas in the remote island country of Zar. The
company’s opertions are regulated by the State Energy Commission. The demand function for gas in Zar has
been estimated as:
P = 1,000 - .2 Q
Where Q is output ( measured in units ) and P is price ( measured in dollars per unit ). Zar Island’s cost function
is : TC = 300,000 + 10 Q
This total cost function does not include a “ normal “ return on the firm’s invested capital of $ 4 million.
(One) In the absence of any government price regulation, determine Zar Island’s optimal
(a)
output level, (ii) selling price, (iii) total profits, (iv) rate of return on its asset base.
(Two) The State Energy Commission has ordered the firm to charge a price which will provide it with no more
than a 12 percent return on its total assets. Determine Zar Island’s (i) output level, (ii ) selling price, and (iii
) total profits under this constraint.
Hint: The roots of the quadratic equation:
Q: A monopolist faces the following total revenue ( TR ) and total cost ( TC ) functions:
TR= 300 Q –0.001 Q2
TC= 9,000,000+20Q +0.0004 Q2
-
-
Calculate the optimal price/ output combinations and determine the monopolist’s
If entry was allowed and a large number of firm entered into the market resulting in a perfectly
competitive setup where the price was fixed at 260; Calculate the optimal price/ output combinations of the
firm and determine its profits.
Compare the results obtained above under monopoly and perfect copetition.
Q :A publishing company produces both hard- cover and paper-back books. Production processes differ in the
amount of Machine time and labor time required with hard-cover books requiring 0.4 hours of machine time and
0.25 hours of labor time. Paper-backs require 0.25 hours of machine time and 0.1 hours of labor time. Hardcover books contribute 8 SR to profits of the firm whereas paper-backs contribute 3 SR to profits. Total
production is limited by available labor time of 400 hours and available machine time of 800 hours. A limited
supply of paper necessary for paper-back publications restricts paper-back production to 3000 copies.
-
Use an appropriate method of solution to find the optimal combination of hard-covers and paper-backs
which will maximize company profits.
Q : Identify each of the following statements as TRUE or FALSE and explain why:
-The coefficient of determination R2
shows the share of total variation in demand that cannot be explained by the regression model.
-
-
The cross-price elasticity of personal computers with software is –4. This means that a 5 % reduction in
the price of personal computers will cause a 20 % increase in software demand.
Decreasing returns to scale and increasing average costs are indicated when EQ < 1
-The marginal cost function derived from a cubic cost function is itself a linear function of output.
-
The Cobb-Douglas production function implies constant elasticities of output with respect to each of the
inputs.
-
An efficiently functioning cartel would tend to equate marginal revenues among its members.
-
Monopolistic competition exists in a market where the product is homogeneous.
-
Linear Programming assumes decreasing returns to scale.
-
Average cost equals marginal cost at the point of minimum efficient scale ( MES ) where average cost
is at a minimum.
Given values for the dependent variable, the estimated demand relation can be used to forecast future values of
demand.