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Understanding more about Consumers

Understanding more about Consumers. Recall the law of demand was a statement that the price of a product and the quantity demanded of the product move in opposite directions. Thus, a higher price means a lower quantity demanded and a lower price means a higher quantity demanded.

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Understanding more about Consumers

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  1. Understanding more about Consumers

  2. Recall the law of demand was a statement that the price of a product and the quantity demanded of the product move in opposite directions. Thus, a higher price means a lower quantity demanded and a lower price means a higher quantity demanded. The authors point out a more general way to state this. They have: People do less of what they want to do as the cost of doing it rises. Implicitly they also mean People do more of what they want to do as the cost of doing it falls. SO, the law of demand we had before used the term price and now the new statement uses the term cost. Cost is a more general term and includes the price. Let’s think about an example.

  3. Let’s say you are sitting in class and you are getting really thirsty. You are really starting to think about that drink of water you can get at the fountain outside of class for a price of $0. (I think we should allow student groups to do fundraisers and allow them to charge a nickel for each 5 seconds a person takes at the fountain – but that is another story.) Scenario 1: You leave class and no one is at the fountain. You take your drink and you skedaddle on down the road. Scenario 2: You leave class and 15 people are in line at the fountain. You say to yourself, “what is going on here, I have schtuff to do.” You do not wait for the drink, you just go. In the second scenario you have too great a cost and thus you do less of the activity – here drinking water.

  4. In economics a major question of interest is How should consumers allocate income among the various goods and services available? We will answer with a relatively simple model that includes the following ideas. Consumers have only two goods to choose from, good x and good y. Consumers only have so much income to spend, and we will have them spend it all. If you want, you can say they have made the decision to save some and then with what is left we look at the decision of how much to spend on x and y. Consumers have to pay a price for each good. Consumers get utility or happiness from consuming goods and they attempt to maximize their utility.

  5. Consumer Behavior • Consumers’ rational behavior leads them to try to maximize their utility through consuming goods. • It is assumed • Consumers know their preferences for products, consumers have only a limited income and must pay prices, and there is a fixed time period set for analysis.

  6. Consumers know their preferences for each product • This assumption is reflected in a consumer’s diminishing marginal utility schedule for each product. • Total utility = utility obtained from the consumption of all units of a good. • Marginal utility = additional utility obtained from the consumption of the last unit.

  7. Example for 1 product Units of good TU Mu 0 0 1 10 10 2 18 8 3 24 6 4 28 4 5 30 2 6 30 0 7 28 -2 Note: Mu is Diminishing, or the additional utility is getting smaller and smaller Note: If more(less) is consumed, the Mu on the last unit consumed gets smaller(larger).

  8. Preferences again • It is assumed that for every product you know about you have a similar marginal utility schedule. It is not exactly the same, but similar. • So, for each good you have a schedule (and we could graph it, if we wanted to.)

  9. Why does marginal utility diminish? WHY NOT! Think about right now. If I had a huge bucket of Snickers (please change the example to have what you like) and you could eat all you wanted you would probably stop after a few. Why? You probably think about things like you are getting filled up, others might be watching you eat, and other stuff. So, eventually more units add happiness, but the additional units are not adding as much happiness as previous units. The point I am trying to make is that we just assume marginal utility diminishes because it seems to make sense with many goods that you and I deal with. Now I am going to have a generic example were for each good there is a TU column and MU column. But, it will not be explicit. You have to use your imagination – you can do it!

  10. Utility maximization rule or Rational Spending Rule • The consumer’s money income should be allocated so that the last dollar spent on each product purchased yields the same amount of extra utility. • MUx/Px = MUy/Py • Spending should be allocated across goods so that the marginal utility per dollar spent on each good is the same for each good.

  11. Example • Say consumer has $400 to spend, x has a price $1 and y has a price of $2. • One way to help us here is to note that each time one y is bought, 2 units of x are given up. • Benefit of taking a unit of y = MU of that unit • Cost of taking y = utility loss from not having 2 units of x.

  12. Let’s see if the consumer would be maximizing utility if they buy 200 units of x and 100 units of y. First, let’s make sure they can buy the combination. If they can not buy the combination then it can not be the one that maximizes their utility given the income and prices they face. 200 x at $1 per unit = $200 100y at $2 per unit = $200 and they total $400. So this is a good “basket” of goods. Now, remember the person has a marginal utility schedule for each good and basically the numbers get smaller the more units of the good the consumer has. Say at 200 units of x the MU = 12 and at 100 units of y the MU = 16

  13. Say at 200 units of x the MU = 12 and at 100 units of y the MU = 16. Say the consumer thinks about the 101st unit of y. This would add a little less than 16 to utility. But 2 units of x have to be given up and thus 12 units of utility on the 1st x given up and probably something close to that on the second unit given up, so it does not make sense to take any more y. What about taking more x? Say the consumer takes 2 more units of x. The utility on each unit are probably less than 12, but when added the amount is probably more than 16. The 16 is the amount of utility given up because the 100th unit of y would not be able to be purchased. So the consumer should take more x and less y.

  14. Example - continued • So, given income, preferences and prices, The amount 200 for x and 100 for y is not the best because the utility gained from taking more x is greater than the utility lost for having less y. • Now, by looking at the MU/P for each good we can arrive at the same result faster.

  15. Example - continued • Faster way • AT Qx=200 and Px = 1, MUx/Px=12/1, and • with Qy=100 and Py=2 the MU/P=16/2 = 8. • Choose combination where MUx/Px=MUy/Py. • If MUx/Px>MUy/Py take more x (which lowers MUx) and less y (which raises MUy).

  16. Another Example Say Tom has $36 to spend, the price of x = $6 per unit and the price of y = $3 per unit. Also say his total utility for each is Qx TUx MUx MUx/Px Qy TUy MUy MUy/Py 0 0 0 1 1 20 1 40 2 38 2 46 3 54 3 50 4 68 4 54 5 80 5 56 6 90 6 57 7 98 7 57 8 104 8 57

  17. So, to figure out the best basket, let’s put in the MU columns first. Here MU is just the additional TU from line to line. So in a given row take the TU in that row minus the TU in the previous row. Note you can’t do MU for a Q = 0 because there is no previous row. Qx TUx MUx MUx/Px Qy TUy MUy MUy/Py 0 0 ----- 0 0 ---- 1 20 20 1 40 40 2 38 38 – 20 =18 2 46 6 3 54 16 3 50 4 4 68 14 4 54 4 5 80 12 5 56 2 6 90 10 6 57 1 7 98 8 7 57 0 8 104 6 8 57 0 Note in general that the MU for each declines or diminishes the more you get.

  18. Finally when we see Px = 6 and Py = 3 we can put in MU/p for each Qx TUx MUx MUx/Px Qy TUy MUy MUy/Py 0 0 ----- --------- 0 0 ---- ---- 1 20 20 20/6=3.33 1 40 40 40/3=13.33 2 38 18 18/6=3 2 46 6 6/3=2 3 54 16 16/6=2.67 3 50 4 4/3=1.33 4 68 14 14/6=2.33 4 54 4 4/3=1.33 5 80 12 12/6=2 5 56 2 2/3=.67 6 90 10 10/6=1.67 6 57 1 1/3=.33 7 98 8 8/6=1.33 7 57 0 0/3=0 8 104 6 6/6=1 8 57 0 0/3=0 Remember that Tom has $36to spend. Note the MU/P column is telling us the marginal utility per dollar spent on a good. It is the proverbial “bang for the buck.” Starting out at 0 units of each which adds more bang for the buck, 1 unit of x or 1 unit of y? 1 unit of y, right?

  19. Now, after taking the first unit of y, Tom spent $3 but he has $36 to spend. So next should he take the second unit of y or the first unit of x? Per dollar spent the first x is better than the second y, right? Sure, 3.33 is better than 2. So now with 1 of each he is spending $9, but has $36, so should his next move be the second x or the second y? The second x because 3 is better than 2. Now with 2 of x and 1 of y he is spending 6(2) +3(1) = 15, but he has $36 so he can spend more. Should he take the 3rd x or the 2nd y? The 3rd x should be taken because 2.67 is better than 2. He would be spending 6(3) + 3(1) = 21, but he has $36 to spend. He should take the 4th x over the 2nd y because 2.33 is better than 2 and then on the 5th x or 2nd y we have a tie and since he can do both let’s have him take both. So now he spends 6(5) + 3(2) = 36, which means he has exhausted his income (an I am exhausted typing this up.) The best basket is 5 of x and 2 of y.

  20. Note TU from both is 80 + 46 = 126. Note also that at this combination the MU/P is equal across both goods when you look at the amount of each purchased. Say someone says that he would be better at 4 of x and 4 of y. What do you say? First can he afford 4 of each? Well 6(4) + 4(3) = 36, so he can buy it. Note MUx/Px = 14/6 = 2.33 > 1.33 = 4/3 = MUy/Py. So the “bang for the buck” is not the same on each good. Take more of x and less of y. When he takes another x he adds a total of 12 units of utility but he must give up 2 units of y and these 2 units have utility of 8 total. So he adds 12 and loses 8 for a net increase of 4 units of utility.

  21. So, what have we accomplished here? Well, in our example with Tom, when he has $36 to spend and the Price of x = $6 and the piece of y = $3 he buys 5 x and 2 y because this combination maximizes his utility. His demand curve for x would show (and there is a similar graph for his demand for y): Now with a price of 6 for x he can buy more x but he doesn’t because the utility he would add with more x is less than the utility he loses because he would have to give up some y. So, what we have added is that he is at this point on the demand curve because he has maximum utility given his income, prices and taste and preferences for various good. P 6 D Q 5

  22. Hey let’s see what happens when we see Px = 5 and Py = 3 we can put in MU/p for each Qx TUx MUx MUx/Px Qy TUy MUy MUy/Py 0 0 ----- --------- 0 0 ---- ---- 1 20 20 20/5=4 **2 1 40 40 40/3=13.33 **1 2 38 18 18/5=3.6 **3 2 46 6 6/3=2 **7 3 54 16 16/5=3.2 **4 3 50 4 4/3=1.33 4 68 14 14/5=2.8 **5 4 54 4 4/3=1.33 5 80 12 12/5=2.4 **6 5 56 2 2/3=.67 6 90 10 10/5=2 **7 6 57 1 1/3=.33 7 98 8 8/5=1.6 7 57 0 0/3=0 8 104 6 6/5=1.2 8 57 0 0/3=0 Remember that Tom has $36to spend. Note the MU/P column is telling us the marginal utility per dollar spent on a good. It is the proverbial “bang for the buck.” Starting out at 0 units of each which adds more bang for the buck, 1 unit of x or 1 unit of y? 1 unit of y, right? I put the **1 meaning do that first. The next purchase is 1 of x. You see the **2, right. SO, you see with the price of x falling more of X would be purchased because more X is part of a now larger amount of utility.

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