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Unformatted text preview: VERSION WITH SOLUTIONS VICTORIA UNIVERSITY OF WELLINGTON FACULTY OF COMMERCE AND ADMINISTRATION SCHOOL OF ECONOMICS AND FINANCE MIDTRIMESTER TEST, 2007 ECON 201: MICROECONOMICS INSTRUCTIONS:
· Duration of test: 50 minutes.
· Total marks: 100, 20 mult iple cho ice quest ions @ 5 marks each.
· Pocket calculators can be used, but not notes or books.
· Please fill in your student ID number and cho ice of answer for each quest ion carefully on the separate onepage answer sheet.
· For any calculat ions, use the back of the question pages, or the margins or any empt y space on the question pages. Only the answer sheet is to be returned at the conclusio n of the test. Question 1 The diagram below shows a change in the equilibrium price and quantit y of co ffee: P B P2 A P1 Q1 Q2 Qcoffee The change could be due to which of the fo llowing? (a) (b) *(c) (d) A failure of the coffee harvest in Brazil which drives up the price A rise in consumers’ inco mes when coffee is an inferior (but not a Giffen) good) A sharp increase in the pr ice o f tea (which is a substitute for coffee) A change in consumer tastes away fro m coffee in favour of wine Note: To get from A to B with “normal” curves requires AT LEAST a demand shift to the right. A rise in the price of a substitute produces such a shift. None of the other shocks do. Question 2 Nonsatiat ion implies that: *(a) (b) (c) (d) Wit h standard convexit y assumpt ions, indifference curves have negative slope Consumers are unable to attain their constrained optimum Marginal ut ilit y is negat ive at the optimum The Marginal Rate of Subst itution of x for y is increasing Note: with convex indifference curves, only the region of negative and diminishing MRS is relevant to a rational consumer. On BB p.79, property 1 of indifference curves is: “when the consumer likes both goods (i.e. when MUx and MUy are both positive) all the indifference curves have a negative slope.” Positive MU equates to nonsatiation. Question 3 At the choke price on a linear demand curve: (a) (b) (c) *(d) Elast icit y o f demand is zero Elast icit y o f demand is (minus) one Elast icit y o f demand is (plus) 100 Elast icit y o f demand is (minus) infinit y See BB pp.4142, and specifically Figure 2.16. Question 4 On the demand curve Q = 600 – 40P, when P = 5, the elast icit y o f demand is (a) *(b) (c) (d) 0.1 0.5 1.25 2.0 When P=5, Q=600200 = 400. Elasticity at this point is ¶Q P P 5 × = 40 × = 40 ×
= 0 5 . .
¶P Q Q 400 Question 5  1 If the demand curve is Q = 6 P 2 and P=37, the elasticit y o f demand is (a) *(b) (c) (d) 1.0 0.5 0.75 3.0 This is a constantelasticity demand curve of the form Q = aP b with elasticity b; there’s no need to calculate anything. See BB p.42 and p.67, Appendix to Chapter 2. Question 6 For two goods i and j the crossprice elast icit y o f demand is: *(a) DQi P j ×
DP Q j i (b) DQi P × i DP Q j i (c) (d) DQi P j ×
DPi Q i DQi Pi ×
DPi Q i BB p.48 equation 2.6. Question 7 A negat ive crossprice elast icit y o f demand between two goods means that the goods are (a) (b) *(c) (d) subst itutes Giffen goods complements nondurable goods BB p.49. Question 8 Consistency o f preferences implies that (a) *(b) (c) (d) If A f B and C f B then A f C If A f B and B f E then A f E If A f C and E p C then A p E If A f B and B p E then the consumer is indifferent between A and E BB pp.123124; the term “transitivity” was used in lectures though it does not appear in the textbook – and the notation should be immediately familiar. Question 9 A consumer’s utilit y funct ion is U=4xy and the prices of the two goods are Px=8 and Py=24. The consumer’s inco me is 1,200. Which of the fo llowing is correct? (a) *(b) (c) (d) The consumer’s optimal quantit y of good x is 50 The consumer’s marginal ut ilit y o f income is 12.5 The consumer’s optimal quantit y of good y is 75 1 The MRSxy at the optimum is /4 Set up the Lagrangian as per BB p.132: L = 4 xy + l (1200  8 x  24 y ) ¶L y = 4 y  8 = 0 Þ l =
l ¶x
2 ¶L x = 4 x  24 = 0 Þ l =
l
and x = 3 y ¶y
6 ¶L = 1200  8 x  24 y = 1200  24 y  24 y = 1200  48 y = 0 ¶l
Þ y = 25 ¹ 75 and x = 75 ¹ 50 Substituting back, λ = 25 ÷ 2 = 12.5 which is the MU of income Question 10 A consumer’s preferences over two goods are represented by: U ( x , y ) = 1 3 2 x y 50 The prices are Px and Py , and an amount of mo ney E can be spent on these goods. The two utilit y maximis ing demand funct ions are: *(a) 6 E 1 E x = × and y = × 7 Py 7 Px (b) 2 E 3 E x = × and y = × 5 Py 5 Px (c) 2 E 1 E x = × and y = × 3 Py 3 Px (d) x = 37 E 3 E ×
× and y = 50 Py 50 Px 1 1 See BB pp.144145, Learning by Doing Exercise 5.2. Given U = × x 3 y 2 , the 50 marginal utilities are MU x = 3 50 1 2 2 x y and MU y = 1  3 2 × x y 1 100 Þ MU x 300 =
×
MU y 50 i i 2 2 2 x y y 3 = 6 x y x At the tangency of the highest indifference curve with the budget P MU x 6 y line, x = =
Þ P x = 6 P y x y P x y MU y Substitute into the budget constraint: 6 Py y + Py y = E Þ P x And Px x + x = E Þ 7 Px x = 6 E Þ 6 x = y = E 7 Py 6 E 7 Px Question 11 0 4 7
Consider the CobbDouglas production function Q = 18 L . K 0. . This is an example o f (a) (b) (c) *(d) Decreasing returns to scale Perfect subst itutabilit y of inputs A Leont ieff production funct ion Increasing returns to scale BB p.211 Learningbydoing Exercise 6.3: a + b > 1 means increasing returns to scale. Question 12 The demand curve for a good is Q = 48,000 – 120P. When the price is $50, consumer surplus is (a) (b) (c) *(d) $14.7 millio n $2.1 millio n $9.6 millio n $7.35 millio n See BB p.160 Figure 5.14. The choke price here is 48,000 ÷ 120 = 400 For P = 50, Q = 48,0006,000 = 42,000 The calculation is CS = (40050)*42,000÷2 = 7,350,000 Question 13 Composite g o o d y M K R E
A C U2 B U 1 xA xC x In the diagram, Co mpensating Variat ion is the distance (a) (b) *(c) (d) KM AB KR BE BB p.161 Figure 5.15. Question 14 In a Leontieff (fixedproportions) production function, the elast icit y o f subst itution is given by (a)
(b) *(c) (d) s = ¥
s = 1
s = 0
1 £ s < ¥ BB p.209 Table 6.6 Question 15 2
A firm has total shortrun cost C = 5q + 90 and half o f its fixed costs are sunk. Its shutdown price is (a) *(b) (c) (d) $20 $30 $35 $40 Shutdown price is the minimum of Average Nonsunk Cost (BB pp.310311). Nonsunk cost here is 5 2 + 45 and Average Nonsunk Cost is q 5 2 + 45 q
= 5 + 45  1 . To find the minimum, differentiate and set to zero: q
q
q 45 45 5  45  2 = 0 Þ q 2 =
q
= 9 Þ q = 3 Þ ANSC = 15 +
= 30 5 3 A N S C = Question 16 The market for widgets is in lo ngrun equilibrium. All suppliers face the same 2
average cost curve, AC = 300 – q + 0.02q . The demand curve is D(P) = 642,000 – 36P. The number of suppliers is (a) (b) *(c) (d) 37,165 21,054 25,266 63,149 Find the Minimum AC at Minimum Efficient Scale for the individual firm by differentiating AC and setting to zero:  1 + 0 04 q = 0 Þ q = 25 and AC = 300  25 + 0 02 * 25 * 25 = 287 5 . . . . When P=287.5, D(P)=642,000 10,350 = 631,650 So the number of suppliers is 631,650 ÷ 25 = 25,266 Question 17 Suppose the production of cars is characterised by the production funct ion
2 L + K Q = L + K , with marginal products MPL = and
L L + K MPK = . The price of labour is $10 per unit and the price of capital is $1 K per unit. If a car manufacturer wishes to produce 121,000 cars, its costminimising quant it ies o f labour and capital will be ) ) ( (a) (b) (c) *(d) ( ) ( L = 100 and K = 10,000 L=121 and K = 1,210 L=1,210 and K = 121,000 L = 1,000 and K = 100,000 Note: this is BB’s problem 7.6 p.254, with model answer on p.692. Question 18 For the production funct ion Q = LK , when the price of labour is w and the price of capital is r, the demand curve for labour is *(a) (b) (c) (d) rQ w r L = Q w wQ L = r L = L = Q w Note: This is BB’s problem 7.9 p.254, with model answer p.692. MU L
K w The tangency condition is = =
MU K L r æ w ö
=> K = ç ÷ L è r ø
æ w ö
æ w ö 2
=> Q = LK = L ÷ L = ç ÷ L ç
è r ø
è r ø
rQ => L=
w Question 19 2
A firm faces the production funct ion Q = L K 3 . The price of labour is w = 10 and the price o f capital is r = 5. The Lagrangian mult iplier in the firm’s cost minimisat ion problem is (a) l = (b) l = *(c) l = (d) l = 1
2 LK 3 5
2
L K 2 5 LK 3 5
3 2 LK Note: from BB pp.256257 we have w = l ¶f ( L , K ) ¶f ( L , K ) and r = l ¶L ¶ K w
r 10
5 =
which in this case means l =
=
; 3 2 2 MU L MU K 2 LK 3 K L 5
the first of these gives l =
.
LK 3 It follows that l = Question 20 K per period Q=100 before technical progress Q=100 after technical progress L per period The technical progress shown in the diagram above is (a) *(b) (c) (d) Capitalsaving Laboursaving Neutral Eliminated by the change in relat ive factor prices Note: see BB pp.214215. ******************************************** ...
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 Fall '10
 PaulClacott
 Microeconomics

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