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Utility

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.

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Utility

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  1. 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

  2. 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

  3. the space Utility Consumption Leisure

  4. 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?

  5. The Function Utility Consumption Leisure

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

  7. View 1 Consumption Utility Leisure

  8. View 2 Utility Consumption Leisure

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

  10. 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 Utility Consumption Leisure

  11. U=6/12 U=1/12 U=9/12 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 Utility Consumption Leisure

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

  13. U=6/12 U=9/12 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 Utility Consumption Leisure U=1/12

  14. U=6/12 U=1/12 U=9/12 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 Utility Consumption Leisure

  15. U=6/12 U=1/12 U=9/12 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! Utility Consumption Leisure

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

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