Consider a two-period economy facing the following budget constraints: Ci +k +b< yı, C2 S2 + (1+r)b, where y is an exogenous endowment and second-period output 2 = Ak" with 0 < a < 1 and productivity A. Note that k is both first period investment and second period capital stock (implicitly assuming full depreciation, o = 1). Also note that initial bo = 0, and hence b is both first-period current account and second-period net foreign assets. 1. Explain how this special environment maps into the general framework of National Income Accounts, and in particular why: ca = y1 – C1 – k = b and caz = rb+ y2 – c2 = -b. Note that ca + ca2 = 0 applies in this model as well. 2. Explain how to derive the intertemporal budget constraint: Ak Y1-k+ C2 Ci + 1+r 1+r 3. Given this budget constraint, characterize the optimal capital investment k of the country and interpret your results (how does optimal k depend on r and A, and why).

Our closed economy has a production function Y = A•F(K,LxE), where Y, K, L, E & A all have their usual meanings as per our lectures & course textbook. Also, this production function exhibits all the usual mathematical/economic properties we usually assume: positive marginal products, diminishing marginal products, complementarity between K & (LxE), and constant returns to scale. The aggregate consumption function depends negatively on the real interest rate, the government budget is balanced initially & the economy is in both a long-run equilibrium and steady state initially. The population growth rate is 2% per year, capital depreciates at a rate of 3% per year, the saving rate is 25% and technology is constant. Suppose the level of labour effectiveness (E) suddenly permanently rises by 10%. a) Use the long-run classical model to determine the qualitative impact of this shock on the long-run equilibrium levels of real output, consumption, investment, real interest…

If long-term property rights of an oil well cannot be guaranteed, how will the extraction rate from the well differ from the efficient extraction rate?

Note: Hand written solution is not allowed.