The literature about tradable credit schemes (TCS) as a demand management system alleviating congestion flourished in the past decade. Most proposed formulations are based on static models and thus do not account for the congestion dynamics. This paper considers elastic demand and implements a static TCS to foster modal shift by restricting the number of cars allowed in the network over the day while remaining easy to understand and implement. A trip-based Macroscopic Fundamental Diagram (MFD) model represents the traffic dynamics at the whole urban scale. We assume the users have different OD pairs and choose between driving their car or riding the transit following a logit model. We aim to compute the modal shares and credit price at equilibrium under TCS. The travel times are linearized with respect to the modal shares to derive the stochastic user equilibrium with low computation times. We then present a method to find the credit charge minimizing the total travel time alone or combined with the carbon emissions. We also show that traffic dynamics and trip heterogeneity lead to different network equilibriums under TCS. It highlights the limitations of classical static representations. The proposed framework is applied to a realistic large-scale scenario: the peak hour (7:00-10:00) in Lyon Metropolis, including 384 200 travelers. Under an optimized TCS, the total travel time decreases by 17% and the carbon emissions by 45% by increasing the PT share by 24 points.