Mid-trimester%20test%20with%20solutions%202007

Mid-trimester%20test%20with%20solutions%202007 - VERSION...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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. ******************************************** ...
View Full Document

Ask a homework question - tutors are online