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José clearly prefers point Q to point P. Now repeat this step-by-step process of decision making with marginal utilities. José thinks about giving up the third T-shirt and surrendering a marginal utility of 20, in exchange for purchasing two more movies that promise a combined marginal utility of 27. José prefers point R to point Q. What if José thinks about going beyond R to point S? Giving up the second T-shirt means a marginal utility loss of 21, and the marginal utility gain from the fifth and sixth movies would combine to make a marginal utility gain of 23, so José prefers point S to R.

However, if José seeks to go beyond point S to point T, he finds that the loss of marginal utility from giving up the first T-shirt is 22, while the marginal utility gain from the last two movies is only a total of 19. If José were to choose point T, his utility would fall to 100. Through these stages of thinking about marginal tradeoffs, José again concludes that S, with one T-shirt and six movies, is the choice that will provide him with the highest level of total utility. This step-by-step approach will reach the same conclusion regardless of José’s starting point.

Another way to look at this is by focusing on satisfaction per dollar. Marginal utility per dollar is the amount of additional utility José receives given the price of the product. For José’s T-shirts and movies, the marginal utility per dollar is shown in [link] .

marginal utility per dollar = marginal utility price

José’s first purchase will be a movie. Why? Because it gives him the highest marginal utility per dollar and it is affordable. José will continue to purchase the good which gives him the highest marginal utility per dollar until he exhausts the budget. José will keep purchasing movies because they give him a greater “bang or the buck” until the sixth movie is equivalent to a T-shirt purchase. José can afford to purchase that T-shirt. So José will choose to purchase six movies and one T-shirt.

Marginal utility per dollar
Quantity of T-Shirts Total Utility Marginal Utility Marginal Utility per Dollar Quantity of Movies Total Utility Marginal Utility Marginal Utility per Dollar
1 22 22   22/$14=1.6 1 16 16 16/$7=2.3
2 43 21   21/$14=1.5 2 31 15 15/$7=2.14
3 63 20   20/$14=1.4 3 45 14 14/$7=2
4 81 18   18/$14=1.3 4 58 13 13/$7=1.9
5 97 16   16/$14=1.1 5 70 12 12/$7=1.7
6 111 14   14/$14=1 6 81 11 11/$7=1.6
7 123 12   12/$14=1.2 7 91 10 10/$7=1.4

A rule for maximizing utility

This process of decision making suggests a rule to follow when maximizing utility . Since the price of T-shirts is twice as high as the price of movies, to maximize utility the last T-shirt chosen needs to provide exactly twice the marginal utility (MU) of the last movie. If the last T-shirt provides less than twice the marginal utility of the last movie, then the T-shirt is providing less “bang for the buck” (i.e., marginal utility per dollar spent) than if the same money were spent on movies. If this is so, José should trade the T-shirt for more movies to increase his total utility. Marginal utility per dollar measures the additional utility that José will enjoy given what he has to pay for the good.

Questions & Answers

explain and give four Example hyperbolic function
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The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
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Source:  OpenStax, Openstax microeconomics in ten weeks. OpenStax CNX. Sep 03, 2014 Download for free at http://legacy.cnx.org/content/col11703/1.2
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