1. Assume an individual has 20 birr to spend on two products: X1 and X2 each with market
price of 2(two) birr. If the total utility the consumer generates from the two products is as
given on the table below,
1.1. Select all combinations of X1 and X2 that fulfill the necessary conditions of consumer
equilibrium, and from them identify the consumer’s equilibrium purchase size (2pts).
Q 1 2 3 4 5 6 7 8 9 10 11
TUX1 16 30 41 51 60 68 75 81 86 89 90
TUX2 15 28 40 48 54 59 63 66 68 69 69
The combinations of X1 and X2 that fulfill the necessary conditions of consumer equilibrium are:
Q1: X1=10, X2=10
Q4: X1=8, X2=12
Q7: X1=6, X2=14
Q9: X1=5, X2=15
The consumer’s equilibrium purchase size is X1=5 and X2=15.
To determine the consumer equilibrium, we need to compare the marginal utilities of the two products with their prices.
Given the total utility values for X1 and X2 as follows:
Q | TUX1 | TUX2
-------------------------------
1 | 16 | 15
2 | 30 | 28
3 | 41 | 40
4 | 51 | 48
5 | 60 | 54
6 | 68 | 59
7 | 75 | 63
8 | 81 | 66
9 | 86 | 68
10 | 89 | 69
11 | 90 | 69
To find out the combinations of X1 and X2 that fulfill the necessary conditions of consumer equilibrium, we compare the marginal utilities (change in total utility) of each product with their prices (2 birr).
For X1:
- The change in total utility from Q1 to Q2 is 30 - 16 = 14
- The change in total utility from Q2 to Q3 is 41 - 30 = 11
- The change in total utility from Q3 to Q4 is 51 - 41 = 10
- The change in total utility from Q4 to Q5 is 60 - 51 = 9
- The change in total utility from Q5 to Q6 is 68 - 60 = 8
- The change in total utility from Q6 to Q7 is 75 - 68 = 7
- The change in total utility from Q7 to Q8 is 81 - 75 = 6
- The change in total utility from Q8 to Q9 is 86 - 81 = 5
- The change in total utility from Q9 to Q10 is 89 - 86 = 3
- The change in total utility from Q10 to Q11 is 90 - 89 = 1
For X2:
- The change in total utility from Q1 to Q2 is 28 - 15 = 13
- The change in total utility from Q2 to Q3 is 40 - 28 = 12
- The change in total utility from Q3 to Q4 is 48 - 40 = 8
- The change in total utility from Q4 to Q5 is 54 - 48 = 6
- The change in total utility from Q5 to Q6 is 59 - 54 = 5
- The change in total utility from Q6 to Q7 is 63 - 59 = 4
- The change in total utility from Q7 to Q8 is 66 - 63 = 3
- The change in total utility from Q8 to Q9 is 68 - 66 = 2
- The change in total utility from Q9 to Q10 is 69 - 68 = 1
- The change in total utility from Q10 to Q11 is 69 - 69 = 0
Now, let's compare marginal utilities with prices:
For X1:
- MUx1(Q1 to Q2) = 14 > 2, continue
- MUx1(Q2 to Q3) = 11 > 2, continue
- MUx1(Q3 to Q4) = 10 > 2, continue
- MUx1(Q4 to Q5) = 9 > 2, continue
- MUx1(Q5 to Q6) = 8 > 2, continue
- MUx1(Q6 to Q7) = 7 > 2, continue
- MUx1(Q7 to Q8) = 6 > 2, continue
- MUx1(Q8 to Q9) = 5 > 2, continue
- MUx1(Q9 to Q10) = 3 > 2, continue
- MUx1(Q10 to Q11) = 1 > 2, stop
For X2:
- MUx2(Q1 to Q2) = 13 > 2, continue
- MUx2(Q2 to Q3) = 12 > 2, continue
- MUx2(Q3 to Q4) = 8 > 2, continue
- MUx2(Q4 to Q5) = 6 > 2, continue
- MUx2(Q5 to Q6) = 5 > 2, continue
- MUx2(Q6 to Q7) = 4 > 2, continue
- MUx2(Q7 to Q8) = 3 > 2, continue
- MUx2(Q8 to Q9) = 2 > 2, continue
- MUx2(Q9 to Q10) = 1 > 2, continue
- MUx2(Q10 to Q11) = 0 ≤ 2, stop
Based on the above analysis, the consumer equilibrium purchase size is Q9, where the marginal utility of X1 is 3 and the marginal utility of X2 is 1. This combination fulfills the necessary conditions of consumer equilibrium.
To determine the consumer equilibrium, we need to find the combinations of X1 and X2 that maximize the total utility generated by the consumer while also considering the budget constraint.
In this case, the consumer has a budget of 20 birr and the market price of each product is 2 birr. So, the consumer can spend a maximum of 10 birr on each product.
To find the consumer equilibrium, we need to compare the total utility generated by each combination of X1 and X2 with the available budget.
From the table given, let's identify the combinations of X1 and X2 where the total utility is within the budget constraint:
Combination TUX1 TUX2
1 16 15
2 30 28
3 41 40
4 51 48
5 60 54
6 68 59
7 75 63
8 81 66
9 86 68
10 89 69
11 90 69
Out of these combinations, let's consider only the ones where the total utility is maximized within the budget constraint.
Combination TUX1 TUX2
5 60 54
Based on the table, the consumer equilibrium purchase size would be X1 = 5 and X2 = 4, as this combination has the highest total utility (TUX1 + TUX2) within the budget constraint.