{"id":9079,"date":"2023-03-10T01:45:45","date_gmt":"2023-03-10T01:45:45","guid":{"rendered":"https:\/\/www.goodacademic.com\/blog\/questions\/utility-functions-marshallian-demand-indirect-utility-expenditure-function-hicksian-demand\/"},"modified":"2023-03-10T01:45:45","modified_gmt":"2023-03-10T01:45:45","slug":"utility-functions-marshallian-demand-indirect-utility-expenditure-function-hicksian-demand","status":"publish","type":"questions","link":"https:\/\/www.goodacademic.com\/blog\/questions\/utility-functions-marshallian-demand-indirect-utility-expenditure-function-hicksian-demand\/","title":{"rendered":"Utility Functions (Marshallian Demand, indirect utility, expenditure function, Hicksian demand)"},"content":{"rendered":"<div class=\"col-sm-12 messageContent\"><b>Learning Goal: <\/b>I&#8217;m working on a micro economics multi-part question and need the explanation and answer to help me learn.<\/p>\n<p>Professor\u00e2\u20ac\u2122s extra explanation and hints: <\/p>\n<p>How do I solve for the Expenditure Function for those dang calculus-unfriendly utility functions in Question 1 ?<\/p>\n<p>Recall what the Expenditure Function, E(p1, p2, U), is supposed to represent: the minimum expenditure necessary for a consumer to be able to achieve consumption worth U utility given prices (p1, p2). For the perfect complement and perfect substitute case, you should be able to solve for that Expenditure Function without using calculus &#8230;<\/p>\n<p>1(a): For the above preferences, the profit maximizing bundle always involves equal amounts of the two goods: x1 = x2. Having more of any one of the goods is a waste as having more of that good does NOT increase utility.<\/p>\n<p>Compare bundle A = {x1 = 4, x2 = 4} with bundle B = ({x1 = 4, x2 = 10}. For both bundles, the utility you get is 4. But bundle B will be much more expensive.<\/p>\n<p>So, you have some income Y to spend on the two goods. And you want the two goods to be the same quantity &#8230; how much would you get of each? Note that Y = p1 x1 + p2 x2. But x1 = x2. So Y = p1 x1 + p2 x1 = (p1 + p2) x1 &#8230; so x1 = ? And therefore x2 = ?<\/p>\n<p>As for indirect utility, if x1 = x2 for profit maximizing bundle then U(x1, x2) = min{x1, x2} = x1 = x2 (for profit maximizing bundle) &#8230; Similarly, if U = 2, then you need x1 = x2 = 2 &#8230; which costs you p1 * 2 + p2 * 2 = (p1 + p2) * 2 &#8230;<br \/>1(c): use Shephard&#8217;s Lemma to derive the Hicksian demand from the Expenditure Function ..<\/p>\n<div class=\"questions-requirements\">\n<p class=\"requirement\">Requirements: As long as the answers are clear there is no need for in depth explanation<\/p>\n<\/p><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Learning Goal: I&#8217;m working on a micro economics multi-part question and need the explanation and answer to help me learn. Professor\u00e2\u20ac\u2122s extra explanation and hints: How do I solve for the Expenditure Function for those dang calculus-unfriendly utility functions in Question 1 ? Recall what the Expenditure Function, E(p1, p2, U), is supposed to represent: [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","meta":[],"disciplines":[696],"paper_types":[],"tagged":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions\/9079"}],"collection":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/comments?post=9079"}],"version-history":[{"count":0,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/questions\/9079\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/media?parent=9079"}],"wp:term":[{"taxonomy":"disciplines","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/disciplines?post=9079"},{"taxonomy":"paper_types","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/paper_types?post=9079"},{"taxonomy":"tagged","embeddable":true,"href":"https:\/\/www.goodacademic.com\/blog\/wp-json\/wp\/v2\/tagged?post=9079"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}