{"product_id":"duality-and-modern-economics-volume-0-9780521336017","title":"Duality and Modern Economics (Volume 0)","description":"\u003cp\u003eDual arguments have become a standard tool for analysis of problems involving optimization by consumers and producers. The principal aim of this book is to provide a fairly systematic yet simple exposition of the basic structure of such arguments. The emphasis is not on providing mathematically general proofs; instead  a geometric approach is used to provide  in an informal way  an intuitive understanding of duality theory. This book introduces the most common alternative ways of representing preferences and technologies  such as indirect utility and distance functions  expenditure and cost functions  and profit and revenue functions. and it discusses the assumptions under which alternative formulations contain precisely the same information. Results such as Roys identity. the Hotelling-Wold identity  and Shephards lemma are fully explained. as are their roles in facilitating analysis of behaviour.\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":45647078883381,"sku":"ByrdShop_0521336015","price":51.29,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9780521336017.jpg?v=1781687995","url":"https:\/\/atxbooks.com\/products\/duality-and-modern-economics-volume-0-9780521336017","provider":"ATX Books","version":"1.0","type":"link"}