The premise of the second partner is the potential for new business does not justify the additional expense to move. The second partner is what some would term 'risk adverse.' In one respect, the second partner is absolutely correct. Moving to a new location does not financially make sense. The second partner calculates the current expenses will not be recouped unless revenue increases to cover the additional and future costs. After all, potential business is not bankable until it becomes a real business!
Where the premise of the second partner fails to make sense is in the analysis of the move just from the perspective of added expense. Expenses rise annually and increasing revenue to cover costs is always a financial reality as well as a risk. Both partners faced a more daunting financial task when the business first began. The risk is far higher in starting a business than moving an ongoing concern to a new location. Updating stationary is a relatively low-cost expense. Rents change from year to year and are a current expense. While potential business is not bankable, moving to a location providing greater exposure and opening into a broader market for an established business usually pays dividends in increased sales.
To convince the second partner, the first partner needs to do some research. For example, the case indicates the market the partnership currently resides in is a smaller market than the proposed move. The question every business has to ask when expanding is the current market potential exhausted? If the answer is yes, then expansion is the only way to grow the business. Businesses that fail to grow ultimately don't succeed in the long term.