The following answer is based mostly on gut-feeling and I urge you to read some of the papers found in the last section to base your decision on something quantifiable.
Having an additional degree in math will be completely irrelevant in the coursework, where your current courses will be sufficient preparation. Indeed, a game theory/advanced econometrics summer course may be more useful as preparation.
Thesis Advisor (+)
The degree will make it easier for you to find an advisor who is willing to invest time in working with you. If you move from a philosophy/math/economics undergrad degree into a top-school economics Ph.D. you will most likely compete for the attention of supervisors with students from Europe and Asia who already have Master's degrees in some field. Some research from the last section of my answer suggests that in most departments a lot of resources are spent on the very best students.
The math degree will be helpful in your research. From the fields you listed as your interests a Master's degree in math does not seem like a bad idea. All fields mentioned are very math-heavy and often use math that is not taught at undergraduate level. However, if you later decide to work in other fields such as macroeconomics, your math Master's will not help you much.
Job Market (+)
Your decision will also affect your job market prospects. The fields you have outlined have a fairly small job market compared to let's say applied econometrics or macroeconomics. If you do not stand out from the crowd it may be difficult to find a position as assistant professor. Thus, having a math master's may help you write an outstanding job market paper. However, you will be older when you enter the market. For very few employers, this may be a secondary criterion.
When you obtain an assistant professor position after your Ph.D., you will need to write a number of strong papers within several years. If you at that point need to acquire additional math skills this will slow down your research in this crucial time.
Lifetime income (--)
You will most likely lose at least one year of income from doing the degree. If your degree is two years or 1.5 years, you may at most be able to make up for one year via a shorter Ph.D. by being more productive. It is not unlikely that you will lose 2 years of income. However, doing the Master's may allow you to enter better Ph.D. programs, write better papers, and achieve a better job placement, earning you more money. But this effect is hard to estimate.
Be sure to check this website to make the right strategic decisions. There is a lot of research on what makes Ph.D. students in economics successful.