Utility Maximization

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Utility Maximization


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Maximizing Utility Per Dollar Spent : Maximizing Utility Per Dollar Spent Lunch is about to become more complicated!!

Maximizing Utility Per Dollar Spent : Maximizing Utility Per Dollar Spent Economists measure overall “happiness” or “satisfaction” in terms of Utility . A fancy way of saying “usefulness”.

Maximizing Utility Per Dollar Spent : Maximizing Utility Per Dollar Spent A specific unit of measurement of Utility is called a “ Util ”. Example: Eating one Hot Dog gives me 10 Utils of Satisfaction . Eating a second Hot Dog gives me 8 Utils of Satisfaction. Eating a 3 rd Hot Dog gives me 6 Utils of Satisfaction. ( Note: Your Utils might be different) Notice how the my Utils decrease as I consume each additional Hot Dog. “Diminishing Marginal Utility”— Each Hot Dog I eat gives me a little less satisfaction than the one I just ate.

Maximizing Utility Per Dollar Spent : Maximizing Utility Per Dollar Spent Using our Hot Dog example let’s define 3 important terms. 1. Total Utility : The sum of all our Utils as we consume Hot Dogs. The first Hot Dog gave us 10 Utils of satisfaction. Our Total Utility after consuming one Hot Dog is 10. The second Hot Dog gave us 8 Utils of satisfaction. Our Total Utility after consuming two Hot Dogs is 18 (10 +8) The third Hot Dog gave us 6 Utils of satisfaction. Our Total Utility after consuming three Hot Dogs is 24 (10 + 8 + 6).

Maximizing Utility Per Dollar Spent : Maximizing Utility Per Dollar Spent Using our Hot Dog example let’s define 3 important terms. 2. Marginal Utility : The change in Total Utility as as we consume each Hot Dog. Simply, the amount of satisfaction we get from consuming an additional unit of a good/service. The first Hot Dog gave us 10 Utils . Total Utility after ONE Hot Dog is 10 Utils . Marginal Utility after one Hot Dog is 10 Utils . The second Hot Dog gave us 8 Utils . Total Utility after two Hot Dogs is 18 Utils . The Marginal Utility of the SECOND Hot Dog is 8 Utils The third Hot Dog gave us 6 Utils . Total Utility after three Hot Dogs is 24 Utils . The Marginal Utility of the THIRD Hot Dog is 6 Utils .

Maximizing Utility Per Dollar Spent : Maximizing Utility Per Dollar Spent Using our Hot Dog example let’s define 3 important terms. 3 . Marginal Utility Per Dollar Spent : This one is tricky. Now we want to consider the amount of utility we are getting from consuming a Hot Dog relative to how much we are paying for the Hot Dog. “How much satisfaction are we deriving from consuming hot dogs PER DOLLAR we spend on buying Hot Dogs”.

Maximizing Utility Per Dollar Spent : Maximizing Utility Per Dollar Spent Using our Hot Dog example let’s define 3 important terms. 3 . Marginal Utility Per Dollar Spent : IMPORTANT FORMULA : Marginal Utility Per Dollar Spent = Marginal Utility/The Price of the Good or Service Our Marginal Utility of consuming one Hot Dog is 10 Utils . If a Hot Dog costs $1.00 then our Marginal Utility per Dollar Spent on Hot Dogs is 10. If a Hot Dog costs $2.00 then our Marginal Utility Spent per Dollar is 5 (10 Utils /$2.00). If a Hot Dog costs $.50 then it is 20 (10 Utils /$.50).

Maximizing Utility Per Dollar Spent : Maximizing Utility Per Dollar Spent Review these 3 definitions if you need to. They are going to be VERY important for this next part of the lesson. We are going to Lunch! We want to put all of this together to see how we can use the concept of Utility to help us to most efficiently spend each dollar we have. On the next slide you will see a chart that as you click through you will see numbers appear. Pay attention to the categories and what each number means as it appears. For Lunch we are going to decide how many Hot Dogs and/or Hamburgers we are going to purchase with $10.00 based on our desire to MAXIMIZE our Utility for EACH DOLLAR WE SPEND.

PowerPoint Presentation : Hot Dogs Hamburgers Maximizing My Lunch Utility Per Dollar Spent Number Total Utility Marginal Marginal Utility of Hot Dogs Utility Per Dollar Spent MU/Price 1 10 Utils 10 10 2 18 Utils 8 8 3 25 Utils 7 7 4 31 Utils 6 6 5 36 Utils 5 5 6 40 Utils 4 4 Number Total Utility Marginal Marginal Utility of Hamburgers Utility Per Dollar Spent MU/Price 1 24 Utils 24 12 2 44 Utils 20 10 3 62 Utils 18 9 4 78Utils 16 8 5 90 Utils 12 6 6 96 Utils 6 3 Price of Hot Dogs = $1.00 Price of Hamburgers = $2.00 Total Utility : Aggregate Total of Utility from consumption of a good/service Marginal Utility: The change in Utility from consuming each ADDITIONAL good/service Marginal Utility Per Dollar Spent : Marginal Utility from consuming each good/service divided By the Price of the Good/Service

PowerPoint Presentation : Hot Dogs Hamburgers Maximizing My Lunch Utility Per Dollar Spent Number Total Utility Marginal Marginal Utility of Hot Dogs Utility Per Dollar Spent MU/Price 1 10 Utils 10 10 2 18 Utils 8 8 3 25 Utils 7 7 4 31 Utils 6 6 5 36 Utils 5 5 6 40 Utils 4 4 Number Total Utility Marginal Marginal Utility of Hamburgers Utility Per Dollar Spent MU/Price 1 24 Utils 24 12 2 44 Utils 20 10 3 62 Utils 18 9 4 78Utils 16 8 5 90 Utils 12 6 6 96 Utils 6 3 Price of Hot Dogs = $1.00 Price of Hamburgers = $2.00 My goal is to maximize my “happiness” or “satisfaction” per dollar that I spend on lunch. Assume I have $10 to spend on Lunch. Which item am I going to purchase FIRST?

PowerPoint Presentation : Hot Dogs Hamburgers Maximizing My Lunch Utility Per Dollar Spent Number Total Utility Marginal Marginal Utility of Hot Dogs Utility Per Dollar Spent MU/Price 1 10 Utils 10 10 2 18 Utils 8 8 3 25 Utils 7 7 4 31 Utils 6 6 5 36 Utils 5 5 6 40 Utils 4 4 Number Total Utility Marginal Marginal Utility of Hamburgers Utility Per Dollar Spent MU/Price 1 24 Utils 24 12 2 44 Utils 20 10 3 62 Utils 18 9 4 78Utils 16 8 5 90 Utils 12 6 6 96 Utils 6 3 Price of Hot Dogs = $1.00 Price of Hamburgers = $2.00 Let’s look at the FIRST line only. Based on “Per Dollar Spent” which food, a Hot Dog or a Hamburger, is going to give you the MOST “Utility Per Dollar Spent”?

PowerPoint Presentation : Hot Dogs Hamburgers Maximizing My Lunch Utility Per Dollar Spent Number Total Utility Marginal Marginal Utility of Hot Dogs Utility Per Dollar Spent MU/Price 1 10 Utils 10 10 2 18 Utils 8 8 3 25 Utils 7 7 4 31 Utils 6 6 5 36 Utils 5 5 6 40 Utils 4 4 Number Total Utility Marginal Marginal Utility of Hamburgers Utility Per Dollar Spent MU/Price 1 24 Utils 24 12 2 44 Utils 20 10 3 62 Utils 18 9 4 78Utils 16 8 5 90 Utils 12 6 6 96 Utils 6 3 Price of Hot Dogs = $1.00 Price of Hamburgers = $2.00 It is going to be a Hamburger. The Hamburger gives me 12 units of satisfaction and the Hot Dog only gives me 10 units of satisfaction. I BUY ONE HAMBURGER! A Hamburger costs $2.00. So far I have spent $2.00. Got it???

PowerPoint Presentation : Hot Dogs Hamburgers Maximizing My Lunch Utility Per Dollar Spent Number Total Utility Marginal Marginal Utility of Hot Dogs Utility Per Dollar Spent MU/Price 1 10 Utils 10 10 2 18 Utils 8 8 3 25 Utils 7 7 4 31 Utils 6 6 5 36 Utils 5 5 6 40 Utils 4 4 Number Total Utility Marginal Marginal Utility of Hamburgers Utility Per Dollar Spent MU/Price 1 24 Utils 24 12 2 44 Utils 20 10 3 62 Utils 18 9 4 78Utils 16 8 5 90 Utils 12 6 6 96 Utils 6 3 Price of Hot Dogs = $1.00 Price of Hamburgers = $2.00 I put a line through the first Hamburger. That is consumed so it goes away and we don’t consider it anymore. Now let’s move down to the second line. We have to decide whether we are going to eat Another Hamburger or eat our FIRST Hot Dog. What do you think??

PowerPoint Presentation : Hot Dogs Hamburgers Maximizing My Lunch Utility Per Dollar Spent Number Total Utility Marginal Marginal Utility of Hot Dogs Utility Per Dollar Spent MU/Price 1 10 Utils 10 10 2 18 Utils 8 8 3 25 Utils 7 7 4 31 Utils 6 6 5 36 Utils 5 5 6 40 Utils 4 4 Number Total Utility Marginal Marginal Utility of Hamburgers Utility Per Dollar Spent MU/Price 1 24 Utils 24 12 2 44 Utils 20 10 3 62 Utils 18 9 4 78Utils 16 8 5 90 Utils 12 6 6 96 Utils 6 3 Price of Hot Dogs = $1.00 Price of Hamburgers = $2.00 This one is a little tougher. Notice the “ Marginal Utility Per Dollar Spent ” for the first Hot Dog is 10 and 10 for the second Hamburger . You get the SAME Utility Per Dollar Spent so you get to choose which one you want to eat next! Lets go for a Hot Dog because you just had a Hamburger. A Hot Dog Costs $1.00. So far you have spent $2.00 for a Hamburger and $1.00 for a Hot Dog For a total of $3.00. Still have $7.00 to go!!

PowerPoint Presentation : Hot Dogs Hamburgers Maximizing My Lunch Utility Per Dollar Spent Number Total Utility Marginal Marginal Utility of Hot Dogs Utility Per Dollar Spent MU/Price 1 10 Utils 10 10 2 18 Utils 8 8 3 25 Utils 7 7 4 31 Utils 6 6 5 36 Utils 5 5 6 40 Utils 4 4 Number Total Utility Marginal Marginal Utility of Hamburgers Utility Per Dollar Spent MU/Price 1 24 Utils 24 12 2 44 Utils 20 10 3 62 Utils 18 9 4 78Utils 16 8 5 90 Utils 12 6 6 96 Utils 6 3 Price of Hot Dogs = $1.00 Price of Hamburgers = $2.00 Now I put a line through Hot Dog number 1. D o we consume a 2 nd Hot Dog or a 2nd Hamburger? 2 nd Hamburger gives us 10 Utils per dollar spent of satisfaction and a Hot Dog only 8. We buy the Hamburger for $2.00 We have eaten 2 Hamburgers and 1 Hot Dog and have spent $5.00 of our $10.

PowerPoint Presentation : Hot Dogs Hamburgers Maximizing My Lunch Utility Per Dollar Spent Number Total Utility Marginal Marginal Utility of Hot Dogs Utility Per Dollar Spent MU/Price 1 10 Utils 10 10 2 18 Utils 8 8 3 25 Utils 7 7 4 31 Utils 6 6 5 36 Utils 5 5 6 40 Utils 4 4 Number Total Utility Marginal Marginal Utility of Hamburgers Utility Per Dollar Spent MU/Price 1 24 Utils 24 12 2 44 Utils 20 10 3 62 Utils 18 9 4 78Utils 16 8 5 90 Utils 12 6 6 96 Utils 6 3 Price of Hot Dogs = $1.00 Price of Hamburgers = $2.00 Put a line through the 2 nd Hamburger Should we eat a 3 rd Hamburger or our 2 nd Hot Dog? The 3 rd Hamburger has a Marginal Utility Per Dollar spent of 9 And the 2 nd Hot Dog has 8. We eat the Hamburger and spend another $2.00 $7.00 spent and $3.00 to go. Getting full yet?? 

PowerPoint Presentation : Hot Dogs Hamburgers Maximizing My Lunch Utility Per Dollar Spent Number Total Utility Marginal Marginal Utility of Hot Dogs Utility Per Dollar Spent MU/Price 1 10 Utils 10 10 2 18 Utils 8 8 3 25 Utils 7 7 4 31 Utils 6 6 5 36 Utils 5 5 6 40 Utils 4 4 Number Total Utility Marginal Marginal Utility of Hamburgers Utility Per Dollar Spent MU/Price 1 24 Utils 24 12 2 44 Utils 20 10 3 62 Utils 18 9 4 78Utils 16 8 5 90 Utils 12 6 6 96 Utils 6 3 Price of Hot Dogs = $1.00 Price of Hamburgers = $2.00 We put a line through the 3 rd Hamburger and move along. Do we consume of 4 th Hamburger or a 2 nd Hot Dog? The Marginal Utility Per Dollar Spent is equal. We get to choose which one again. Let’s eat a 2 nd Hot Dog! Hot Dogs are $1.00. We have spent $8.00 of our $10.00

PowerPoint Presentation : Hot Dogs Hamburgers Maximizing My Lunch Utility Per Dollar Spent Number Total Utility Marginal Marginal Utility of Hot Dogs Utility Per Dollar Spent MU/Price 1 10 Utils 10 10 2 18 Utils 8 8 3 25 Utils 7 7 4 31 Utils 6 6 5 36 Utils 5 5 6 40 Utils 4 4 Number Total Utility Marginal Marginal Utility of Hamburgers Utility Per Dollar Spent MU/Price 1 24 Utils 24 12 2 44 Utils 20 10 3 62 Utils 18 9 4 78Utils 16 8 5 90 Utils 12 6 6 96 Utils 6 3 Price of Hot Dogs = $1.00 Price of Hamburgers = $2.00 We put a line through the 2 nd Hot Dog. Do we consume of 4 th Hamburger or a 3 nd Hot Dog? The Marginal Utility Per Dollar Spent on a Hamburger is 8 and for a Hot Dog it is 7. Hamburgers win again. Hamburgers are $2.00. We have spent $10.00 of our $10.00!

PowerPoint Presentation : Hot Dogs Hamburgers Maximizing My Lunch Utility Per Dollar Spent Number Total Utility Marginal Marginal Utility of Hot Dogs Utility Per Dollar Spent MU/Price 1 10 Utils 10 10 2 18 Utils 8 8 3 25 Utils 7 7 4 31 Utils 6 6 5 36 Utils 5 5 6 40 Utils 4 4 Number Total Utility Marginal Marginal Utility of Hamburgers Utility Per Dollar Spent MU/Price 1 24 Utils 24 12 2 44 Utils 20 10 3 62 Utils 18 9 4 78Utils 16 8 5 90 Utils 12 6 6 96 Utils 6 3 Price of Hot Dogs = $1.00 Price of Hamburgers = $2.00 We put a line through the 4 th Hamburger. We are done! We have spent all our money on the combination of Hot Dogs and Hamburgers that gives us the MOST Utility Per Dollar spent as we consumed each one. So, eating 4 Hamburgers and 2 Hot Dogs Maximized our Utility Per Dollar Spent.

PowerPoint Presentation : Hot Dogs Hamburgers Maximizing My Lunch Utility Per Dollar Spent Number Total Utility Marginal Marginal Utility of Hot Dogs Utility Per Dollar Spent MU/Price 1 10 Utils 10 10 2 18 Utils 8 8 3 25 Utils 7 7 4 31 Utils 6 6 5 36 Utils 5 5 6 40 Utils 4 4 Number Total Utility Marginal Marginal Utility of Hamburgers Utility Per Dollar Spent MU/Price 1 24 Utils 24 12 2 44 Utils 20 10 3 62 Utils 18 9 4 78Utils 16 8 5 90 Utils 12 6 6 96 Utils 6 3 Price of Hot Dogs = $1.00 Price of Hamburgers = $2.00 You will NEVER think of Lunch the same again. 

Another way to look at the same thing… The Utility Maximizing Formula : Another way to look at the same thing… The Utility Maximizing Formula Marginal Utility of Good 1 Price of Good 1 Marginal Utility of Good 2 Price of Good 2 The Goal: Consume the good that gives you the MOST Utility per Dollar Spent relative to the other good you are consuming. If the ratio is not equal, then you CONSUME an additional unit of the good that Gives the GREATER utility per dollar spent. When the ratio are equal then you have “ Maximized Utility”.

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