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Boris lives for two periods and has the following lifetime utility function U(co,c) = u(co) + Bu(ci) In the first period of his life he makes wo. 100,000, and in the second period he earns Wi= 150,000. He is born with no initial wealth, ao = 0, and because of Brexit interest rates are high at 50% (that is, r = 0.5). The budget constraints he faces then read as Co + a1 100,000 150,000 + 1.5a1 C1 1. Derive the intertemporal budget constraint. 2. Use the result from the previous item to set up the Lagrangian and derive the Euler equation for this model. 3. Now assume log-utility, that is, let u(c) = ln(c). Further assume B = 0.8. Derive the optimal choices for co, ci and a1. Is Boris a borrower or saver? 4. For a general utility function u(c) and with an interest rate of 50% and B = , determine the optimal choice of for co, C and a1. You have to show your work. 5. For an interest rate of r = 80%, how patient does Boris have to be (i.e. what must be his B) such that his growth rate of consumption remains the same as in the previous question? Boris lives for two periods and has the following lifetime utility function U(co,c) = u(co) + Bu(ci) In the first period of his life he makes wo. 100,000, and in the second period he earns Wi= 150,000. He is born with no initial wealth, ao = 0, and because of Brexit interest rates are high at 50% (that is, r = 0.5). The budget constraints he faces then read as Co + a1 100,000 150,000 + 1.5a1 C1 1. Derive the intertemporal budget constraint. 2. Use the result from the previous item to set up the Lagrangian and derive the Euler equation for this model. 3. Now assume log-utility, that is, let u(c) = ln(c). Further assume B = 0.8. Derive the optimal choices for co, ci and a1. Is Boris a borrower or saver? 4. For a general utility function u(c) and with an interest rate of 50% and B = , determine the optimal choice of for co, C and a1. You have to show your work. 5. For an interest rate of r = 80%, how patient does Boris have to be (i.e. what must be his B) such that his growth rate of consumption remains the same as in the previous question?