{"id":217721,"date":"2025-05-22T11:28:43","date_gmt":"2025-05-22T11:28:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=217721"},"modified":"2025-05-22T11:28:45","modified_gmt":"2025-05-22T11:28:45","slug":"a-ferry-in-boston-harbor-travels-between-hingham-south-of-boston-and-rowes-whar","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/22\/a-ferry-in-boston-harbor-travels-between-hingham-south-of-boston-and-rowes-whar\/","title":{"rendered":"A ferry in Boston Harbor travels between Hingham (south of Boston) and Rowes Whar"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">A ferry in Boston Harbor travels between Hingham (south of Boston) and Rowes Wharf (downtown Boston). A monthly pass on this ferry costs $329. The Massachusetts Bay Transit Authority (MBTA) is considering increasing the price for the monthly pass by 6.7%. Currently the MBTA sells 2,819 monthly passes on this route to commuters.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a. An estimate for the price sensitivity of commuters to the monthly pass price is e= -0.9. If this is the case, how many monthly passes will be sold if the price is raised by 6.7%?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b. Is the current revenue with the pass price of $329 higher or lower than the expected revenue if the price is increased by 6.7%?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c. If the -0.9 estimate is a short run elasticity, what is the expected long run number of passes sold and expected revenue if long run e= -1.2?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To answer these questions, we\u2019ll use the <strong>price elasticity of demand formula<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\text{% change in quantity demanded} = e \\times \\text{% change in price}<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$e$ = price elasticity of demand<\/li>\n\n\n\n<li>% change in price = 6.7% = 0.067<\/li>\n\n\n\n<li>Current price = \\$329<\/li>\n\n\n\n<li>Current quantity = 2,819 passes<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>(a) New quantity of passes sold with price increase of 6.7% and e = -0.9<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\%\\text{\u0394Q} = -0.9 \\times 0.067 = -0.0603 \\text{ or } -6.03\\%<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\text{New quantity} = 2819 \\times (1 &#8211; 0.0603) = 2819 \\times 0.9397 \\approx 2,648 \\text{ passes}<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <strong>Answer (a): About 2,648 monthly passes will be sold.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>(b) Compare revenue before and after price increase<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Current Revenue:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\text{Revenue} = 329 \\times 2819 = \\$926,451<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>New Price =<\/strong> $329 \\times 1.067 = 351.04$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>New Revenue:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>351.04 \\times 2648 \\approx \\$929,548.90<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <strong>Answer (b): New revenue (\\$929,548.90) is slightly higher than current revenue (\\$926,451), so expected revenue increases.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>(c) Long-run scenario with e = -1.2<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\%\\text{\u0394Q (long run)} = -1.2 \\times 0.067 = -0.0804 \\text{ or } -8.04\\%<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\text{New quantity} = 2819 \\times (1 &#8211; 0.0804) = 2819 \\times 0.9196 \\approx 2,593 \\text{ passes}<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>\\text{New revenue (long run)} = 351.04 \\times 2593 \\approx \\$910,186.72<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 <strong>Answer (c): In the long run, about 2,593 passes will be sold, and revenue will fall to about \\$910,187.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300+ words)<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This problem revolves around <strong>price elasticity of demand<\/strong>, which measures how sensitive consumers are to price changes. A negative elasticity (like -0.9 or -1.2) implies that as price increases, demand decreases.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In part (a), the elasticity is -0.9, and the price is increased by 6.7%. Using the elasticity formula, we calculate that the demand will fall by about 6.03%. Multiplying this decrease with the original quantity sold (2,819), we find the new estimated number of passes to be about 2,648.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In part (b), we compare total revenues before and after the price hike. Initially, the MBTA earns \\$926,451 per month. After the price increase to \\$351.04, even with the drop in quantity to 2,648, the new revenue slightly increases to \\$929,548.90. This demonstrates that, in the short run, the demand is inelastic (|e| &lt; 1). This means commuters don\u2019t significantly reduce their purchases in response to price increases, so revenue rises.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In part (c), elasticity is -1.2 in the long run, meaning demand becomes more elastic (|e| &gt; 1). Consumers have more time to adjust, possibly finding alternative transportation or remote work options. The 8.04% decline in demand leads to 2,593 passes sold, resulting in a revenue of about \\$910,187\u2014<strong>lower than both the current and short-run revenues<\/strong>. This indicates that long-term price hikes can backfire, especially when the good or service is more elastic over time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In summary, while a price increase may generate more short-run revenue, the long-run response may lead to reduced total revenue if commuters become more price-sensitive. This is crucial for MBTA\u2019s pricing decision<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/image-51.png\" alt=\"\" class=\"wp-image-217722\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A ferry in Boston Harbor travels between Hingham (south of Boston) and Rowes Wharf (downtown Boston). A monthly pass on this ferry costs $329. The Massachusetts Bay Transit Authority (MBTA) is considering increasing the price for the monthly pass by 6.7%. Currently the MBTA sells 2,819 monthly passes on this route to commuters. a. An [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-217721","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217721","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=217721"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217721\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=217721"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=217721"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=217721"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}