5.1 - MA160 Section5.1Worksheet Name 54:2. va'ihza An...

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Unformatted text preview: MA160 Section5.1Worksheet Name 54:2.» va'ihza An Economics Application: Consumer Surplus and Producer Surplus The equilibrium point is the intersection of the demand curve D(x) and the supply curve S(x). Solve the equation D(x) = S(x) to get the x-coordinate of the equilibrium point. Consumer Surplus: Suppose that p = D(x) describes the demand fimction for a commodity. Then the consumer surplus is defined for the point (Q, P) as If D(x)dx — 91’ or If[D(x) — PM: . Producer Surplus: Suppose that p = S(x) is the supply function for a commodity. Then the producer surplus is defined for the point (Q, P) as QP — If S(x)dx or If [P ~ S(x)]dx . 1. Given the demand curve D(x) : (Jr—10)2 and the supply curve 80:) = x2. a. Determine the equilibrium point by solving algebraically. (X‘J0323xa' 3. J00 '1'. fwww :- ___...... _, 7‘ view-r1003); /' fig” (5‘, 395‘) 0 art-flag“, Sc 1"; £00-30); 5 ”b “:35 b. On the same graph, Show the arm represented by consumer surplus and the area represented by producer surplus c. Find the consumer surplus at the equilibrium point. . 5' 5" C. 5. :7 f9 £Cx-u:\-26'Jdl : f5(KI—-.).ax1—ma——a5') ctr.— a .— 5" “I (13#10x+75)£13_ :3 25.3.. __ QOXL 5' 0 3 3 :2 +75}, 0 ._ 5' A v .— --10CS) +7915) - - L16 3 0-— r-Qso-rB’I-s': 599.. ¥ 3 3 _ Made? d. Find the producer surplus at the equilibrium point. ‘5‘ 2 3 5 2 u S.': -" d _" ._. q..—-—o- - P £025 1)x..;251 ”al-35cg)__§.5 0 -: “13—5—25" I25” 3 .. To .1 $93.33 2 2 2. Giventhe demand curve D(x)=75—x? andthe supply curve S(x):3~;x-u+x+33. J a. Determine the equilibrium pointbysolving algebraically. é; 75'5;=a_£z+g+3770:xl+x-HA D(élr75‘§:75-ra:é3 5 0 = - l l ’7 5 -: Xl‘i- x-t-SB ‘13:}. (1 Fifi; _ (4) 54:3) J - b. Onthe same graph, Show the area represenfed y consumer a ._ . . . . ,. .- surplus and the area represented by producer surplus 70 Mymhfl ..... . ........ .' ' c. Find the consumer surplusatthe equilibrium point. 60 %%%%%%C 1' #3) 6.5.: ,L; - e e. Inn- '1‘ ' la (75' we‘vsldxafo (/2- é—xfiix gal-'1 as. . _ :mxw—‘roxgé’ . 3 4n 1' .«7 3 ‘3'" 0-” lléélva-(é ):71-2q: $92 an _..._. d. Find the producer surplusatthe equilibrium point. 6 1 . 6 _ F. S. :. Léfé3- 3;- +x+333dx:£ [63- 2:: y}; x-BBJdp :f (39—?)8‘... x)dvx 3 e a s1 3' :3035...-—-—--_7_(___..}_l 0 i. 3 3 3 .. sate) flaw, 32(6)“: [£0.—¢f§-)?: ‘qu Answers WS 5.1 1b. a. .J rug-Fl. "'I o / we r‘ ' f ' ,r 7 ‘. *fi‘fi ms" " "flirt 1“"‘3 §w§§gfa la. (5, $25) 1c. $166.67 1d. $83.33 filfli‘l . am: 5“ am; “\‘mfl 413 'm1\ .. 3E| Za. {6, $63) 20. $48 2d. $114 7:... r . " k I; '- qfifis \ww a .5 :33 ...
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