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18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 303 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 304 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 305 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 306 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 30 "Consumer and Producer S urplus " }}{PARA 261 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 54 "Suppose that a manufacturer produces widgets and that " }} {PARA 262 "" 0 "" {TEXT -1 84 "the demand curve (i.e. the selling pr ice for x widgets in a fixed period of time)" }}{PARA 263 "" 0 "" {TEXT -1 12 " is given by" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT -1 38 "p(x) = 100 - x , where 0 < x < 100." }} {PARA 265 "" 0 "" {TEXT -1 0 "" }}{PARA 266 "" 0 "" {TEXT -1 80 "On th e other hand ther eis a curve called the suppply curve which describes the " }}{PARA 267 "" 0 "" {TEXT -1 91 "minimum price that the supplie r will require to produce widgets in a fixed period of time." }} {PARA 268 "" 0 "" {TEXT -1 0 "" }}{PARA 269 "" 0 "" {TEXT -1 33 "Assum e a supply curve is given by" }}{PARA 270 "" 0 "" {TEXT -1 0 "" }} {PARA 271 "" 0 "" {TEXT -1 41 "s(x) = 10 + x^2/100, where 0 < x< 100 . " }}{PARA 258 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 0 " " }}{PARA 260 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "p := x -> 100 - x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "s := x -> 10 + x^2/100;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot([p(x), s(x)], x=0..100);" }}}{EXCHG {PARA 272 " " 0 "" {TEXT -1 106 "Observe that the demand curve and the supply cur ve give the same price value when x is approximately 57." }}{PARA 274 "" 0 "" {TEXT -1 0 "" }}{PARA 275 "" 0 "" {TEXT -1 36 "The supply \+ and demand at 57.25 are :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalf(p(57.25));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalf(s(57.25));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f := x -> 42.7;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "plot([p(x),s(x),f(x)],x=0..60, color = [black, red, b lue]);" }}}{EXCHG {PARA 276 "" 0 "" {TEXT -1 53 "The blue line is call ed the fair market price P=42.7." }}{PARA 277 "" 0 "" {TEXT -1 0 "" }} {PARA 278 "" 0 "" {TEXT -1 87 "If the consumer buys widgets according \+ to the demand curve, then the consumer pays more" }}{PARA 279 "" 0 "" {TEXT -1 45 "than the fair market price for Q=57 widgets." }}{PARA 280 "" 0 "" {TEXT -1 0 "" }}{PARA 281 "" 0 "" {TEXT -1 104 "If the sup plier sells widgets applying the supply curve values, then the supplie r makes less money than " }}{PARA 282 "" 0 "" {TEXT -1 36 "if the fair market price is charged." }}{PARA 283 "" 0 "" {TEXT -1 0 "" }}{PARA 284 "" 0 "" {TEXT -1 0 "" }}{PARA 285 "" 0 "" {TEXT -1 95 "If the prod ucer and the consumer would agree that the fair price is this point of intersection," }}{PARA 286 "" 0 "" {TEXT -1 32 "then they would both \+ save money." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 287 "" 0 "" {TEXT -1 35 "The consumer surplus is defin ed by " }}{PARA 288 "" 0 "" {TEXT -1 0 "" }}{PARA 289 "" 0 "" {TEXT -1 27 "CS = int(p(x) - P, x=0..Q)" }}{PARA 290 "" 0 "" {TEXT -1 0 "" }}{PARA 291 "" 0 "" {TEXT -1 39 "and the producers surplus is defined \+ as" }}{PARA 292 "" 0 "" {TEXT -1 0 "" }}{PARA 293 "" 0 "" {TEXT -1 29 "PS = int(P - s(x), x=0..Q). " }}{PARA 295 "" 0 "" {TEXT -1 0 "" }} {PARA 294 "" 0 "" {TEXT -1 30 "Maple will do the calculations" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "evalf(int(p(x) - 42.7, x=0..57.25));" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 36 "evalf(int(42.7 - s(x), x=0..57.25));" }}}{EXCHG {PARA 296 "" 0 "" {TEXT -1 60 "Now repeat this calulation for the fol lowing two problems: " }}{PARA 304 "" 0 "" {TEXT -1 2 "1)" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 297 "" 0 "" {TEXT -1 22 "p := x -> 400 - x^2, " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 299 "" 0 "" {TEXT -1 18 "where x < 20 and " }}{PARA 301 "" 0 "" {TEXT -1 0 "" }}{PARA 300 "" 0 "" {TEXT -1 24 "s := x-> 4 + 2*x^2. " }}{PARA 306 "" 0 "" {TEXT -1 0 "" }}{PARA 305 "" 0 "" {TEXT -1 2 "2)" }}{PARA 303 "" 0 "" {TEXT -1 0 "" }}{PARA 302 "" 0 "" {TEXT -1 47 "p := x -> 1000 - 10*x^ 2, and s := x -> x^3" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ":" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }