Directions for Experiment 3

There are seven rounds in the experiment. In each round, you will be given a budget to spend on two** **commodities, X and Y, and you will be told prices for X and Y. You have to determine the amount of X you want to purchase __relative __to the amount of Y you want to purchase. Thus, you do not have to specify** **how much of each good you want to purchase but only the ratio of the quantity of X you wish to purchase** **to the quantity of Y you wish to purchase.

You are rewarded according to the level you attain plus a commission on the number of units of good X you purchase. The levels are defined as follows. Level 1 is composed of the following combinations of good X and good Y, with the level of good X listed first:

Level 1: (1,120) (2,90) (3,65) (4,45) (5,30) (6,18) (7,11) (8,6) (9,3) (10,2.50) (11,2.25)

There are an infinite number of other levels. All these other levels are composed of points which are** **simple multiples of the points on Level 1. For example, the points on Level 2 are the same as those on Level 1 except each combination of X and Y is multiplied by 2:

Level 2:(2,240) (4,180) (6,130) (8,90) (10,60) (12,36) (14,22) (16,12) (18,6) (20,5) (22,4.5)

To illustrate further, Level 4, for example, is composed of the same points as Level 1 except each combination of X and Y on Level 1 is multiplied by 4:

Level 4: (4,480) (8,360) (12,260) (16,180) (20,120) (24,72) (28,44) (32,24) (36,12)

(40,10) (44,9)

In this manner, there are an infinite number of levels, each composed of multiples of the points on Level 1.

To attain a level, you must purchase a combination of good X and good Y that either lies on the level or** **contains at least as much of both good X and good Y as one of the points on the level. For example**, **suppose you purchase the combination (16,11). Since the point (7,11) is on Level 1, this would qualify** **you for Level 1. Since there is no point on Level 2 with 16 or less units of good X and 11 or less units of good Y, it does not qualify you for Level 2. Hence the level attained from 16X and 11Y is Level 1.

On each round, the reward you receive for the combination of good X and good Y you purchase equals $.20 times the level you attain plus a commission of 1 cent on each unit of good X you purchase. For example, suppose the price of X is $20, the price of Y is $1, and your budget is $250. You would be** **asked to specify the ratio of the quantity of good X to the quantity of good Y you wished to purchase. Suppose you selected the ratio of 4X to 45Y. The cost of 4 units of X would be $80 and the cost of 45 units of Y would be $45, so the total cost of 4X and 45Y would be $125. Since your income is $250, this** **means that at a ratio of 4X to 45Y, you could purchase a total of 8X and 90Y. Examining the level** **schedules, this would put you on Level 2, hence you would earn 2 x $.20, or $.40, from attaining Level 2. In addition, you would buy a total of 8 units of good X (level 2x4X), which would provide you with a** **commission of 1 cent x 8 or $.08. Hence your total profit for that round of the experiment would be $.48.

In each round of the experiment, you will be given a budget and a price of X. Write these down in the table on the last page under the columns labeled Budget and Px respectively. The price of Y will be fixed** **at $1 for all rounds and thus it will not be reported on each round. All you have to do is choose the ratio** **of the quantity of good X to the quantity of good Y you wish to purchase. To simplify the experiment, you can choose from only the 11 ratios that define Level 1. These include 1X:120Y, 2X:90Y, 3X:65Y, 4X:45Y, 5X:30Y, 6X:18Y, 7X:11Y, 8X:6Y, 9X:3Y, 10X:2.50Y, 11X:2.25Y. When you have decided on the ratio of good X to good Y you want, record it in the table under the column labeled Q_{X}:Q_{Y} You do not need to** **record the symbols X and Y, just the numbers in the ratio you chose. For example, if you chose the ratio 8X:6Y, just record 8:6.

Once the experiment begins, you will be given only a few seconds to choose the ratio of good X to good Y for each round. Consequently, you will not have time to do any calculations. You need to determine in** **advance some kind of rule you are going to use to choose the ratio of good X to good Y. You will have a** **few minutes before the experiment begins to determine your rule.

When all seven rounds of the experiment are completed, you will tally your profits by filling in the remaining entries in the table. First, for each round you will determine the cost of the ratio of good X to good Y you have chosen. For example, if the price of X equalled $3 and you selected the ratio of 5X:30Y, then the cost of this combination would be $3 x 5 + $30 x 1 = $45. Then you would divide your budget by this cost to determine the level you again. For example, if your budget was $9O. the level you would** **attain would be $90/$45, or Level 2. If this number is not a whole number, round it to the smallest integer. For example, if your budget had been $150, $150/$45 = 3.33 and you would have attained Level 3. Enter** **this level in the table under the column labeled Level. Next ascertain the quantity of good X you** **purchased by multiplying the numerator in the ratio you selected by the level you attained. In the above example, if you chose 5X:30Y and had a budget of $90, the quantity of good X would be 5 x 2 = 10. Record this amount in the column labeled Q_{X}. Then add the levels attained on all seven rounds, and** **enter the total at the bottom of the column labeled Level. Similarly, add the quantity of X purchased in all** **seven rounds and enter the total at the bottom of the column labeled Q_{X}.Then multiply the total Level by .20 and the total Q_{X} by 1 cent and enter the sum at the bottom of the table next to Total Profits. Hand in only the sheet with your calculations at the end of the experiment. Make sure you have recorded your** **name and section in the space provided above the table.

Name Section

As a reminder, the possible ratios of Q_{X} to Q_{Y} you can choose from are, as itemized on Level 1: 1:120, 2:90, 3:65, 4:45, 5:30, 6:18, 7:1 1, 8:6, 9:3, 10:2.50, and 11:2.25.

Round |
Budget |
P |
Q |
Level |
Q |

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2. |
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3. |
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4. |
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5. |
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6. |
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7. |

Total Level Total Q_{X}

Total Profits