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380 test 1 key short

# 380 test 1 key short - Exam 1-Winter 2010 Economics 380 R...

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Unformatted text preview: Exam 1-Winter 2010 Economics 380 R. Pope Name Sits-4%.--. Throughout, the notation is as we have used in class: EJ‘is a utility function, x and y are two goods with respective prices, p)( and by, and l is income. Show your work. Total: 140 points (listed beside each question). (5) 1. List and explain 3 main axioms that are used to obtain a utility function representation of preferences: 1- 4:0“; w Era as!» ewe. Q; Vt’l‘i‘irtu .2.” FM“; I? ‘3‘“ 5 mama-Mia 1‘9“ ., M ‘ .‘ lzmgﬁt («gﬁsm E» 2")“ )- 8» z... 3* . .. «my». .jésm kgﬁﬁ/‘uﬁnnﬁinﬂcw WQMAWV‘ J “a: (15) 25) Explain the meaning of the marginal rate of substitution (MRS). b) Does the utility function lJ(x,y)=y+6ln(x) have diminishing MRS (y on the vertical axis). c) Why does diminishing . - MRS hold special interest? ’ ‘ 1: .n’ -.-' .‘ . a" A w. , .. . .,,...:2,,. .v r {5.1 . 1" i. , M", .' ’ w " -.' r) sit/ciaﬂgsim {fat-,WEammteesmﬂ 5,» I. g . . ' ‘ ﬁg on Hfisﬁtaﬂwtﬁtswamp. a; t t“ Jg ﬁUQQw'thgémwwkaamﬁféﬁw ' “ N (10)3. ﬁbn is in'sc’ ofoﬁ work. His job allows ﬁ'e’xible hours and he is paid \$9 per hour. Write his wéekly budget . constraint between leisure (x) and goods (y) in the form that economists prefer. «ﬁll—l; llas 0” y 40 iiiér WEEK thagfghe can dividinbgtwleen'leisure anti-‘55g “*4 twat»ch all a 3.. L54" Mm»an mrwﬁteé} ¢ I t v, “m k s a L4! .53: cl 3; t1 5} ﬁt 4) E . M . ' Irma ‘ menﬂg‘ k hgﬁgdgﬁrg -- - - has: i V 7 w : er s” - . ’ K} g . I _ H. I. r) ' _ . x CT 7 . its"? «Maid- i. _ .. (15) 4: Explain why the following utility ngtion's represents or does not represent the same I. preference ordering: (x, y) = xay” ; -U(JE, yj --—5"1'0'+ a1n(x) + ,6 1n( y) ? ‘ ’mllg‘sm "3 ii leis/M M3552; = aw): 3/9/33: 0’ let/ﬁx, ﬁjwﬂgaﬁm is. . ‘ _ Matti team alt...) «ii—4%. <l> It“ New? s Wage; aw maﬁa“ '- ’ ‘ ' aw»; Fig.1.! ‘.- m’w’é , -./. . ' . .3 v . (35) 5. If Sally s FuMllty function for transportation (y) and ﬁtness (x) is U(x.,.y.)—= 1l(x:—10)y and the budget constraint is left: general: pxx+ pyy S I ' (5) 3. Using Lagrange’s method, write the Lagrangian for this problem. Xvi I: (meagié: 5-f-‘RKEM {3x X’figsxér W W 3??" b. Write the first order conditions. 2:; a Miter/93W 5 will, it .. S, a“); .9139 a? "Fa . (S) c. After eliminating the multiplier (x7. ), what are the two equations which must be solved togetdeﬁhzsz 2; . V .1 3 gr} (10) d. Explain the meaning of one of the first order conditions in terms of marginal cost and marginal benefit of consumption of x. :9. : MRSCMSKUWD-mmﬂﬁﬁa Mm. ’ ' - i. . , . AK. __ _:, i?- ty I 5 We I? ’4’ \~ E 14‘; W"£~§J~\$~w M -- W M C" \Ea -Mas§;m Awwr mm =21 Wﬂlgx >Mg§za «9/0 WAQX , 7% B MRsﬁ-Mﬁg 4‘ mag/y £3? * 'Q. _MCD%WX. g '17ng ﬁt c, mbwmgxzm, :3}; m . zip: ,.-mxX-‘?’£)rm3:~ml #5 .?A>‘lpt&¢ x“ (a 5 _ I _. (Ewing/a? ; Kt) w :2 [1 @lgcy‘gﬁg f (25) 6. Maximization utility U = xryw gives rise to demand function: (10) e. Calculate the demand functions fortrans ortation and itn’ess. X PX X w; x*=;/—{~, Px (10) a. What is the income elasticity ofdemand? Is this goodnormai? \$X1l: 75’ ‘ Eye, 2:“: I. 2/ z: \$wa'ﬁ 'w .~ 75" 7 W‘ ’7'; TS“ “gs-Fat? ﬁaﬂlﬁ A 731: x . >4 a “6’ - ' ‘ -" . - . P)! g, f ﬁﬂwgg-ﬁmj; magma? . WW” ,. w- la ' 1:: :3“ iii) a” -- I; * (5) b. Would this dem nd function generate a reasonable ngel curve for food? Explaiﬁ; E . 'l I. V‘ I N83 '9'; ' view“? voxmgtw 5w ‘32, w: :5; A i t. wig éwmm ‘ " ‘- " '5‘” x . E YL at [/\k 0 ' we (10) c. What is the own—price elasticity of demand? (write the deﬁnition and the result). Does this good satisfy the "law of demand”? ,~ . ‘ a - 5 it .3” m” X 1:; gal}: W655i: rm lg :3 ﬁxm. "f"wg,~ﬁ<%:z: ﬁt: I . (10) 7. If the’second demand function in 6. is y* = (1—y)—, what is the form and m : hing of . a ' 29,, the indirect utility function? , . " J r» " . 3" “gauuarwgﬁﬁma we?) Wﬁﬁié} . .-< . I ’ I ' I (10) 8. Thinking of homogeneity, would the "demand function” ln(x*) = 3px /py +21 be a reasonable form if deri d frm Utility mainlization subject to a budget constraint? Explain. Magi/- “a . ~ to . , - , .- Q i ‘ _l ‘3 Kai» ' W? L“? unca5 (15) 9. John utili ti4.-n is of the form U(x,y)=min('x/2,y/3). ‘ any given level of utility U, say U=100, what will it costJohn to attain that utility with prices px and py? leﬁzﬂ’ ' i szl, Pt}le a3 at E ;ﬁu5®+3m;7m Wt a“ ~~ W "3 gnaw X .t at. :5; in.” “3w 5» .w M‘ J mum-0‘ 49".: ' . < ~- fi _MMM|H»H,H‘anm\$meﬂ§;!:§l 6 x» "*1- ‘ I "> XV-wamjri)? 7‘73qu 2 ‘ U 7px If: a Wig") 7”" , ' : \'. ‘ If” ‘- r o yaw MW» ﬁvw’U-fﬁﬂ (wwmf vuﬁwrswmﬂﬂfwyfmﬁw t ...
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