In this homework I choose the economical curve is the total utility curve.
A curve illustrating the relation between the total utility obtained from consuming a good and the quantity of the good consumed. The shape of the total utility curve, increasing at a decreasing rate, reflects the law of diminishing marginal utility. The reason for this is that slope of the total utility curve is marginal utility, meaning the total utility curve can be use to derive the marginal utility curve.
| Q | Total Utility | Marginal Utility | P |
| 0 | 0 | ||
| 1 | 11 | 10 | 5 |
| 2 | 20 | 8 | 4 |
| 3 | 27 | 6 | 3 |
| 4 | 32 | 4 | 2 |
| 5 | 35 | 2 | 1 |
| 6 | 36 | 0 | 0 |
| 7 | 35 | -2 |
In this case, the total utility have the binomial expression: y=-x^2+12x.
According to the Q=2, we find a linear y=9x+2 which connect with the point(2,20) in the second graph.
If we find countless linear to connect with total utility graph, we can find the slope of the total utility.
The marginal utility actually is the slope of total utility, the linear expression of marginal utility is y=-2x+12.
We can see that when marginal utility equal to 0, that total utility achieve to the max.
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