In models of monocentric cities, property prices must decrease proportionally with the distance from the city center to compensate for the increase in the cost of transportation (as demonstrated in the pioneering work of Alonso [1960] or Fujita [1989]). In traditional models, costs of transportation are assumed to be known and fixed. However, the gas prices can be fluctuant and thus significantly change the costs of transportation for households and their living expenses. In a zone that is characterized by limited access to employment, a household faces a greater uncertainty in transportation expenses during recessions especially if they have to search out other employment opportunities in the case of being fired. They may take this into account when renting or purchasing a property. In following Scafuri(1984), bid functions can be derived as a function of expected transportation cost and variance. Using time series, for housing and transportation price in personal vehicles in France, we test whether the difference in prices between city center and suburb vary in congruence with expected transportation costs and their volatility. A vector error correction model (VECM) is estimated. The estimated results indicate the existence of a co-integrated relationship: the differences in price between the center and the suburb tend to grow with the volatility of transportation costs. The results bring the first empirical elements that confirm the importance of the uncertainty of transportation costs. The prices to the city center tend to fluctuate with the level of transportation costs and with their volatility. Households asks for a risk premium in the suburbs to pay for reduced transportation costs and volatility compared to the households that live in the city centers.