Problem Solving – Econometrics

Answer all of the following questions and submit your assignment by 4:00 pm on the due
date through UM Learn. Please get in touch with me via email with any questions.
1. Express each of the following in summation notation (i.e. they should look like the
questions in question (2) below). (1 mark each)
(a) y2 + y3 + y4 + y5
(b) y2 z2 + y3 z3 + y4 z4 + y5 z5
(c) a4 b43 + a5 b52
(d) (z3 +y3 ) + (z4 +y4 ) + (z5 +y5)
2. Expand each of the following sums (i.e. when you “expand” them they should look like
what you see in question (1), above, except that you should get an actual number for
questions (a) and (c) below. (1 mark each)
(a) ∑ (#
$%& 𝑦 ( + 𝑦 + 5)
(b) ∑ 𝑓(𝑧, 𝑥)0
1%&
(c) ∑ 2𝑧 + 1(
1%0
3. Based on years of a mild caffeine addiction and a very keen sense of observation, your
professor has determined the probability distribution function of x, the number cars in the
drive–through line at 8:00 am to be as follows:
x 0 1 2 3 4 5 6
f(x) .005 .025 .310 .340 .220 .080 .020
(a) Sketch the probability density function for X (2 marks)
(b) Find the probability that on a given day more than 3 cars will be in line (2 marks)
(c) Compute the expected value of the random variable X. Interpret this result. (3 marks)
(d) Compute the variance and standard deviation of X (2 marks each)

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4. Please list the following information. (1 mark each)
(a) Why you chose your current major (Agribusiness for most of you).
(b) Your favourite U of M professor/class so far and why.
(c) What you want to do as a career.
(d) What do you consider to be your greatest accomplishment to date.
(e) Who is the most interesting person you ever met and why.
(f) What is the most fun you have ever had.
5. Following the example from the notes in Lecture 1, come up with an interesting/fun
econometric example (like when we wrote out the Maple Leaf pork demand example in
econometric notation). It does not have to be complicated and it should be something that
interests you. Define each of your variables. (5 marks)
6. Given the following observations (x,y): (3,5); (2,2); (1,3); (–1,2); and (0,–3), find the
following by hand (no calculator permitted – show all of your work) (15 marks):
a) ∑ 𝑥 4
0 , ∑ 𝑥 4 𝑦4 , ∑ 𝑥 4 , ∑ 𝑦4 , 𝑥̅ , 𝑦6 (1 mark each)
b) 𝑏& and 𝑏0 (2 marks each)
c) Graph 𝑦< = 𝑏& + 𝑏0 𝑥 4 (2 marks)
d) Interpret the meaning of 𝑏& and 𝑏0 (1 mark each)
e) Suppose that you know the value of the intercept is zero ( 𝛽& = 0). Derive the new
equation for 𝑏0 . (Hint @A
@B = −2 ∑ 𝑥 4 𝑦4 + 2𝛽 ∑ 𝑥 4
0 ) (4 marks)
f) Using your answer from part e) calculate 𝑏0 using the (x,y) pairs above (2 marks)
7. A company receives deliveries of a particular component from three suppliers. The
following table gives the number of good and defective parts from each supplier as a
proportion of total parts received.
Component Supplier
A B C
Good 0.36 0.38 0.16
Defective 0.04 0.02 0.04
(a) If a component is selected at random from all those received, what is the probability
that it is defective? (2 marks)
(b) What is the probability that a component from supplier A is defective? (2 marks)
(c) Is the quality of the component independent of the source of supply? (2 marks)

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(d) What is the probability that a randomly selected component is from supplier C? (2
marks)
8. One way of valuing the recreational–use benefits of national parks is to estimate the
consumer surplus associated with a demand function that relates number of visits to a
park to a hypothetical entry price. Lack of data on the number of visits for different entry
prices can be a problem, but it can be overcome using the so–called “travel cost method.“
To utilize this method, data on number of visits and on travel costs (i.e. how much it costs
the person visiting the park to get there) are collected, and it is assumed that consumers of
recreation react to changes in a hypothetical entry price in the same way as they would to
changes in travel costs. Beal (1995) utilizes the travel cost method to estimate the value
of Carnarvon Gorge National Park (Queensland, Australia) for recreational use. Her data
(8 observations) on number of camping visits demanded (Q) for different entry prices (P)
is stored in the file surplus.dat on the course homepage. The unit of measurement for the
observations on Q is thousands of visits per year.
(a) Use least squares to estimate a linear demand equation that relates Q to P. (3 marks)
What is the predicted number of visits for a zero entry price? (2 marks) If price increases
from zero to $10, what is the estimated change in the number of visitors per year? (2 marks)
(b) Estimate the consumer surplus as the total area underneath the demand curve. (3
marks