Why is the nature of graph of utility function different from indifference curve? - Economics Stack Exchange most recent 30 from economics.stackexchange.com 2022-01-17T11:00:56Z https://economics.stackexchange.com/feeds/question/32490 https://creativecommons.org/licenses/by-sa/4.0/rdf https://economics.stackexchange.com/q/32490 0 Why is the nature of graph of utility function different from indifference curve? Shakeel Holmes https://economics.stackexchange.com/users/8566 2019-10-29T17:13:05Z 2019-10-30T07:43:20Z <p>I am new to Economics, but I have this doubt. The indifference curve and utility function both have the same equation, so their graph must also be similar, which is true I guess. Then why is it that the nature of graphs are different? I mean why is it that if the indifference curve is convex then utility function is quasi concave? How did we arrive at this conclusion?</p> https://economics.stackexchange.com/questions/32490/-/32491#32491 4 Answer by Giskard for Why is the nature of graph of utility function different from indifference curve? Giskard https://economics.stackexchange.com/users/1601 2019-10-29T17:28:16Z 2019-10-29T17:28:16Z <p>You seem to be confusing some things.</p> <blockquote> <p>The indifference curve and utility function both have the same equation</p> </blockquote> <p>The utility function has a formula, not an equation.</p> <p><span class="math-container">\$U(x_1,x_2)\$</span> is a utility function.</p> <p>The points <span class="math-container">\$(x_1,x_2)\$</span> for which <span class="math-container">\$U(x_1,x_2) = 13\$</span> form an indifference curve. (13 was picked as a random number)</p> <p>The graph of a utility function has one more dimension than the graph of an indifference curve: in addition to the space of goods, this graph would also include the utility value, so its points would be something like <span class="math-container">\$(x_1,x_2,u)\$</span>. Chances are you have not seen a graph of any such function, as 3D drawings are complicated. This is why maps of 2D indifference curves are used to get a feeling for the shapes of utility functions. </p> https://economics.stackexchange.com/questions/32490/-/32495#32495 1 Answer by keepAlive for Why is the nature of graph of utility function different from indifference curve? keepAlive https://economics.stackexchange.com/users/10247 2019-10-30T02:01:59Z 2019-10-30T07:43:20Z <p>Utility functions and indifference curves are the same object considered from different visual/conceptual angles. Below an illustration on <span class="math-container">\$U(x_1, x_2) = x_1^{0.5} x_2^{0.5}\$</span> (representing <em>Cobb-Douglas preferences</em>), done with excel:</p> <p><a href="https://i.stack.imgur.com/dImU3.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/dImU3.png" alt="enter image description here"></a></p>