I am having difficulty understanding your question. Is your dependent variable the land area that has been developed? Is your independent variable the total land area in the city?

My dependent variable is the land area that has been developed, and my independents conclude the economic variables like GDP. I consider the rightness to use the area as the dependent variable. Because each city has different administration area. I think the proportion is more proper. I also find someone said that some people don't use the logarithmic transformation for the marginal efficiency. But I con't find some related papers. And I am not sure to use logarithmic transformation with my dependent variable.

Let's start at the very beginning. You need to be testing an hypothesis. So where do you get an hypothesis? Find several published papers that deal primarily with a particular hypothesis. These papers may differ with respect to their conclusions. Why do they differ? Well, the data may differ or the form of their model may differ. It sounds to me like you are looking toward cross-sectional data, so it may be that you are doing this for different cities in a country. Perhaps others have looked at other countries. It is possible that in other countries there are different proportions of undeveloped land within cities . . . perhaps there are different regulatory climates or something like that. So maybe the proportion of land area that is developed could be a function of the rigor of the regulatory climate. This would require you to have a proportion on the left hand side of the estimating equation. This would be a limited dependent variable. As a result, you might consider first converting the variable to the odds of being developed (divide the proportion developed by the proportion undeveloped) and then take the log of that. So the bottom line is that you might very well be well-advised to use a log transformation.

Thank you very much for your answer! I think for a long time for that and I agree with you.