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1 ECON 301 – LECTURE #9 ROBINSON CRUSOE ECONOMY In this economy, Robinson Crusoe plays a dual role: he is both the only producer and the only consumer. He can choose to spend his time getting a tan on the beach (consuming leisure) or he can spend it gathering coconuts. The more coconuts he finds, the more he has to eat but the less time he has to work on his tan. We know that Rob will have preferences over coconuts and leisure represented by some utility function. He will also have some production function that represents the relationship between how much he works and how many coconuts he can get. This production function is likely to be one with diminishing marginal returns to labour. Given these two bits of information, we can find out how much Robin works and how many coconuts he will have (his general equilibrium). This is simply the tangency between his production function and his family of utility curves, point (C*,L*) below. So, at (C*,L*) the slope of the indifference curve must be equal to the slope of the production function by the standard logic that if they crossed, there would be some other feasible point that is preferred. Coconuts Labour L* C* Production Function Indifference Curves
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2 This means that the marginal product of labour must equal the marginal rate of substitution between leisure and coconuts. Great! But now the story takes a little twist… Since Robby is stranded on an uncharted island, he might get a little…eccentric (insane). So suppose he decides that he is now not simply one person that just happens to be both the producer and consumer for the economy, but rather he is two people (split personality?) one of which is the consumer and the other being the producer. In order to facilitate transactions Bob decides to set up a labour market and a market for coconuts. He sets up a firm, “Bobby C’s Inc.” and becomes the sole shareholder. This firm considers the prices for labour and for coconuts when deciding how much labour to hire and how many coconuts to produce. The firm is guided by the principles of profit maximization when making these decisions. Robinson, in his role as the worker, will collect income from working which he will use as his constraint as the sole consumer when he decides how many coconuts to buy. Bobby C, in his role as the firm’s sole shareholder will collect the firm’s profits. In order to keep track of the transactions, Bobby C and Robinson come to an agreement on a currency called sand-dollars, or dollars for short. They also agree that one coconut will be worth one dollar (numeraire good = coconuts). Now all they need to agree on is a wage rate… We want to consider this “economy” after it has been established and has been operating for a period of time and everything has settled into an equilibrium. In this equilibrium state, the demand for coconuts equals the supply of coconuts and the
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