Utility This slideshow is to help you –Visualize the utility function as a three dimensional object –Relate the two dimensional indifference curves to the utility function

space First, we need to set up a way of representing utility as a function of consumption and leisure. –the vertical axis (up-down) denotes the level of utility Higher = greater utility –the axis that points into the screen denotes consumption “deeper” = more consumption –the axis that points to the right denotes leisure Further to the right = more leisure

Consumption Leisure Utility the space

function We know utility is an increasing function of both consumption and leisure: –U(C,Leisure) Lets assume a specific functional form: What does this function look like?

Consumption Leisure Utility The Function

Consumption Leisure Utility Let’s rotate the graph in a few directions to understand it’s shape better: View 1 View 2

Consumption Leisure Utility View 1

Consumption Leisure Utility View 2

Consumption Leisure Utility Now let’s find the indifference curves: Put lines on the surface of the curve for specific levels of utility

Consumption Leisure Utility Now let’s find the indifference curves: Put lines on the surface of the curve for specific levels of utility – every line traces out all the combinations of consumption and leisure that give a fixed level of utility

Consumption Leisure Utility Now let’s find the indifference curves: Put lines on the surface of the curve for specific levels of utility – every line traces out all the combinations of consumption and leisure that give a fixed level of utility U=1/12 U=6/12 U=9/12

Consumption Leisure Utility U=1/12 U=6/12U=9/12 Removing the rest of the curve, leaving only these lines

Consumption Leisure Utility Removing the rest of the curve, leaves only these lines, and giving them some color so we can distinguish between them If we take the “shadows” that these lines would cast on the bottom square, they still contain all the information of the utility curve U=1/12 U=6/12U=9/12

Consumption Leisure Utility Removing the rest of the curve, leaves only these lines, and giving them some color so we can distinguish between them If we take the “shadows” that these lines would cast on the bottom square, they still contain all the information of the utility curve U=1/12U=6/12U=9/12

Consumption Leisure Utility Removing the rest of the curve, leaves only these lines, and giving them some color so we can distinguish between them If we take the “shadows” that these lines would cast on the bottom square, they still contain all the information of the utility curve So we need only look at the Two dimensional versions Indifference Curves! U=1/12U=6/12U=9/12

Consumption Leisure U=1/12U=6/12U=9/12 Indifference Curves