1. Consider the small open economy version of the Solow growth model. The constant-returns-to-scale production function is given by: Y = F(K, AL). (1) Labor and technology grow over time according to L (t) = L(0) ent (2) and A (t) = A(0) est, (3) respectively. The first new feature relative to the closed economy ver- sion of the model is the difference between production (GDP) and income (GNP) determined by interest payments on net foreign assets B. The second new feature is that the interest rate r is exogenous and equal to the world interest rate. For simplicity, we will assume that the world interest rate, and thus r, remains constant. Income is now given by: X = Y+rB. (4) Furthermore, wealth is defined as: W = K +B. (5)Gross investment is given by: I = K +6K. (6) In the closed economy version of the Solow model, it is assumed that a fixed proportion 0 0. Using the expressions derived above, derive and sign dk*, dy*, dw*, db*, da*, de*, di* and de* . Note that we have to assume that ng-or > 0. This is a stability condition that ensures that w converges to w* starting from an initial value w (0). Furthermore, it is important to distinguish between two cases depending on whether &* is above or lower than its golden-rule level. In Case 1, &* is lower than its golden-rule level and r >n+g. In Case 2, k* is higher than its golden-rule level and r n+9+6, while Case 2 corresponds to f' (k*)