3.1 Robinson Crusoe Economy and the consumption/leisure choiceIn this chapter we abandon growth in favor of short-run cycles. We looked at the factors contributing to the increase of output per capita over the long run. Now, we analyze the factors causing short-run deviations from the long run output trend we studied in Chapter 2. Specifically, we will consider the effect that productivity shocks and changes in wages have on output on the short run. As usual, we simplify our analysis by considering a simple economy with one worker/consumer where there is no investment (I), no government spending (G), no net exports (NX): today we want to isolate the short-run effects that wages changes and productivity shocks have on output through consumption only. This one-consumer economy can be thought of as Robinson Crusoe economy. This model assumes that there is one agent in the economy, Robinson Crusoe, who lives isolated in an island where the only consumption goods are fish. The problem is that fish do not appear randomly in order for Robinson to consume them. He has to work to get fish and he consumes every fish he collects because there is no freezer were he can store them1and also there is nobody else with whom he can trade the fish he catches2. Differently from Solow-Swan, we will allow Robinson Crusoe the CHOICE OF WORK EFFORT (remember that we forced everybody to work all the time in Solow Growth Model). We will allow for work choice because we want to allow for fluctuations in output and we know that labor fluctuates a lot over the business cycle. Therefore, we are in a very simplified model were the economy is closed; there is no government and no investment. Recall the national account identity: ? = 𝐶 + 𝐼 + 𝐺 + ??So under our assumption we have ? = 𝐶3.2 Production and Income: The Resource Constraint. 1 We assume this goods are non storable. 2 The fact that fish are non storable and that Robinson does not have anyone with whom he can trade means that he has no access to the Credit Markets. That is, since fish are non storable, Robinson cannot save them for later or trade them with anybody else. It also means he lives a “static” world where he has no choice to take decisions today to affect his future. We will later relax these assumptions in Chapter 4.