der flex rates, moving the economy from the sticky-rates competitive equilibrium (squares line)to the flex-rates competitive equilibrium (triangles line). Then, the policy-maker imposes a dis-tortionary tax on debt (t) to restore the efficient level of borrowing, moving the economy to theconstrained efficient equilibrium (dashed line).As shown in equation 15, the optimal level oftis zero when the constraint never binds and posi-tive when the constraint is expected to bind with positive probability in period 1. Figure 5 showsthat wheneebthe triangles line and dashed line coincide. However, whene>ebthe tax onborrowing is positive, borrowing in period 0 is lower than in the flex-rates competitive equilib-rium (upper-right panel of Figure 5), while consumption in period 1 is larger (lower-right panel ofFigure 5). That is, whenever the collateral constraint is expected to bind with a positive probabil-ity, the policy-maker forces private agents to borrow less in period 0 —therefore increasing theirnet worth next period— and to consume more in period 1, thereby reducing the probability of afinancial crisis.Note here that, like before, in the flex-rate equilibrium the net worth (and the crisis probability) islower (higher) than in the sticky-rate one because of the higher debt repayment in period 1. Withflexible interest rates, borrowing is lower but it is more costly to service, so net worth in period 1is lower and the probability of a crisis is higher. Adding the tax on debt curtails borrowing with-out increasing debt service costs. As the maximum size of the endowment shock increases, theoptimal level of debt falls. And above a certain threshold, the crisis probability falls even belowthe one in the sticky-rate equilibrium.Consider now a negative shock to the risk-free interest rate (Figure 6). To address the pecuniaryexternality, the policy-maker can impose a tax on debt whenever there is a positive probabilitythat the constraint will bind in period 1 regardless of the sign of the shock. To address the interestrate rigidity, when a negative shock hits the economy, the policy-maker can lower interest ratesbyy. In this case —and differently from a positive shock to the risk-free rate— achieving theflex-rate equilibrium already reduces the probability of a crisis, as the economy moves from thesticky-rates competitive equilibrium (squares line) to the flex-rates competitive equilibrium (tri-angles line). This is because the higher borrowing than in the sticky-rate case is more than com-pensated by the lower interest payment. So, when the policy maker uses also the tax on debt, theprobability of a crisis decreases even more relative to the sticky-rate case, and it is always belowit.In summary, with two instruments, such as a tax on borrowing and the monetary policy inter-est rate, a policy maker can address both the financial and the macroeconomic friction, therebyachieving constrained efficiency, independently of the sign of the shock hitting the economy.