The table below gives an individual\'s marginal utility schedule for good X and
ID: 2507006 • Letter: T
Question
The table below gives an individual's marginal utility schedule for good X and good Y. Suppose that X and Y are the only goods available, the price of X and the price of Y are $1 and the individual's income is $8 per time period and is all spent.
Q
MUx
MUy
1
11
19
2
10
17
3
9
15
4
8
13
5
7
12
6
6
10
7
5
8
8
4
6
Totals
60
100
a. Indicate how this individual should spend his/her income in order to maximize total utility. Justify your answer.
b. What is the total amount of utility received by the individual when in equilibrium? Justify your answer.
c. State mathematically the equilibrium condition for this individual.
Q
MUx
MUy
1
11
19
2
10
17
3
9
15
4
8
13
5
7
12
6
6
10
7
5
8
8
4
6
Totals
60
100
Explanation / Answer
So you want to reach the highest MU as you can when X =$1 Y = $1 and she has a total of $8 to spend.
So you can buy any 8 items of X and Y.
a. She would buy 6 units of Y and 2 units of X. Then all of her $8 would be spent and she would have a unitlity of 107, which is higher than if she bought all Y or all X. ( y= 19+17+15+13+12+10= 86 then x= 11+10=21 86+21= 107 unility).
b. Total equilibrium is 100
c. So the equation is MUx/Px = MUy/Py or 11/1 = 19/1 ---> 11=19 or 11<19 so she chooses Y and her budget goes to $8-$1 = $7
Then you do the same for the second row, 10 = 17 ---> 10 < 17 so she chooses Y and her budget decreases $7 - $1 = $6
And the pattern continues to the point where she only buys all Y in equilibrium, which does not maximize her utility.
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