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chapter3_Robinsin_Crusoe

# chapter3_Robinsin_Crusoe - Disclaimer These notes were...

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Disclaimer: These notes were prepared based on lectures of Prof Sala-i- Martin’s 2008 Fall Course of Intermediate Macro-W3213. Contents of these notes might not match completely with the current teachings in class. An updated version would be available later in the semester. 3.1 Robinson Crusoe Economy and the consumption/leisure choice In this chapter we abandon growth in favor of short-run cycles. We consider a simple economy with one worker/consumer and there is no I, no G, no NX. 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 coconuts. The problem is that the coconuts do not fall from the tree randomly in order to Robinson to consume them. He has to work to collect coconuts and he consumes every coconut he collects because there is no freezer were he can store them and also there is nobody else with whom he can trade the coconuts he collects. Differently from Solow-Swan, we will allow Robinson Crusoe the for 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 cycle. Therefore, we are in a very simplified model were the economy is closed; there is no government and no investment. Recall that the national account identity: ? = ? + 𝐼 + 𝐺 + 𝑁? So under our assumption we have ? = ? 3.2 Production and Income: The Resource Constraint. We consider the following cases (a) Constant Wage Model with No Wealth : ? = 𝑤𝐿 [The Budget/Resource Constraint] (This equation says our income( Y) equals our wage rate (w) times the labor (L) provided). Where w is the CONSTANT wage rate. THIS CONSTRAINT TELLS US WHAT IS FEASIBLE: we can choose to work 24 hours and get lots of cookies OR we can choose zero hours and get zero cookies. You can work any amount in between and get some middle amount of cookies. The person (Robinson Crusoe) has no wealth to begin with. Note that in this simple case with no I, G or NX, C=Y. So we can rewrite the resource constraint as: ? = 𝑤𝐿 3.1 If the guy has NO WEALTH how does the resource constraint (Eqn 3.1) look like in the Consumption Labor plane?

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C ? = 𝑤′𝐿 ? = 𝑤𝐿 L 24 Fig 3.1 It is a straight line through the origin. This is because if we work L=0, we get zero income and if we work L=24, we get maximum income and in this range as L increases y increases. An increase in the wage rate from w to 𝑤′ represents an increase in the slope of the curve, but the curve (line) still goes through zero. (b)Constant Wage Model with Wealth : If the guy has some WEALTH, then he has resources without having to work. The resource constraint becomes: ? = 𝑦 + 𝑤𝐿 3.2 C ? = 𝑦 + 𝑤𝐿 ? = 𝑦 + 𝑤𝐿 𝑦 y L 24 Fig 3.2
This means that the “resource constraint” does not go through the origin; it has an intercept of y.

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chapter3_Robinsin_Crusoe - Disclaimer These notes were...

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