FOUNDATIONS OF ECONOMIC AND FINANCIAL MODELS EMET1001
FOUNDATIONS OF ECONOMIC AND FINANCIAL MODELS
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FOUNDATIONS OF ECONOMIC AND FINANCIAL MODELS
EMET1001
Information and instructions:
• The exam begins at 6:40 pm Canberra time. The duration is 90 minutes (including ’read-
ing time’) plus 10 minutes for scanning and uploading your answers. Hence, the exam
finishes at 8:10 pm and you must submit your answers by 8:20 pm.
• If you take more time, the maximum total mark will be reduced by 1 point per minute you
submit after 8:20 pm. That is, your final mark will be the minimum of the sum of your
points and the maximum total mark as determined by the time we receive your submission.
• Students with special exam arrangements and longer writing times should follow the in-
structions they received by email.
• Permitted materials include all course materials (textbook, exercises, notes) and non-
programmable calculators, but no Internet browsing and no collaboration of any kind.
• Attempt to answer all questions. Show your workings for all questions. The maximum for
this exam is 54 points. Partial credit is given for partial answers. Illegible or ambiguous
answers will get 0 points.
• You must submit handwritten answers and workings as a single pdf file through the Tur-
nitin link on the Wattle course page. Please see the ‘Week 7’ block on the Wattle course
page for instructions on how to create and upload your answer file.
Advice:
• The exam is long, so use your time wisely!
Page 1 of 3 — FOUNDATIONS OF ECONOMIC AND FINANCIAL MODELS — EMET1001
Question 1 [6 points] A firm has two plants A and B located 60 kilometres apart at the two
points (0,0) and (60,0). See the figure below. The two plants supply one identical product
priced at $p per unit. Shipping costs per kilometre per unit are $10 from A and $5 from B. An
arbitrary purchaser is located at point (x,y).
(a) Give economic interpretations of the expressions p+10
√
x2+ y2 and p+5
√
(x−60)2+ y2.
(b) Find an equation for the curve that separates the markets of the two firms, assuming that
customers buy from the firm for which total costs are lower.
Question 2 [9 points]
(a) Find the domain of g(x) =
ln(x−4)
x−7 . If not defined for all real values, explain why some
values are excluded.
(b) Find the values of k that make the polynomial q(x) divide the polynomial p(x) where
p(x) = x2− kx+4, q(x) = x−2.
(c) Let f (x) =
ax+b
cx−a , where a, b, and c are constants, with c ̸= 0 and a
2+bc ̸= 0. Assuming
that x ̸= a/c, show that f ( f (x)) = x.
Question 3 [6 points]
(a) Suppose f (x) = x2+2x. Compute lim
h→0
f (2+h)− f (2)
h
using first principles.
(b) Find the derivative of φ defined by φ(p) = ep ln(p2+2).
Question 4 [9 points] Let f be defined by f (x) = x+4/x.
(a) Find the domain D of f and, if some x are not in D, explain why that is.
(b) Derive f ′(x).
(c) Derive f ′′(x).
(d) Find where f is increasing/decreasing. Explain your reasoning.
(e) Examine where f is concave/convex. Explain your reasoning.
Page 2 of 3 — FOUNDATIONS OF ECONOMIC AND FINANCIAL MODELS — EMET1001
Question 5 [6 points] Suppose a graph is given by x2y+3y3 = 7.
(a) Find the slope of the tangent to the graph at (x,y) = (2,1).
(b) Find y′′ at (x,y) = (2,1).
Question 6 [3 points] Find the differentials:
(a) d(
√
1+ x2). (b) d[ln(1− x3)].
Question 7 [6 points] Evaluate the limits (if they exist)
(a) lim
x→2+
x2−3x+14
x+2
. (b) lim
w→0
(w+8)3−83
w
.
Question 8 [9 points]
(a) Find the domain of β (x) =
x2
2e2x−4ex−6. If not defined for all real values, explain why
some values are excluded.
(b) Determine the limit (if it exists) lim
x→0
ex−1− x
x
√
1+ x− x .
(c) Show that
√
bex ≤ 12(ex+b), where b≥ 0.