LT19 - Robinson Crusoe Economy PDF

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LT19 - Robinson Crusoe Economy ● ● ● ● ●

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One person in economy - Robinson Two goods - Coconuts and leisure Two problems: Robinson the Consumer and Robinson the producer Robinson should aim for pareto efficient allocation Only one person, so pareto efficiency corresponds to the allocation where robinson maximize his utility At a pareto optimum - MRS = MRT Marginal rate of substitution MRS - Rate at which a consumer is willing to exchange one good for another (slope of indifference curves) Technical rate of substitution TRS - Rate at which a firm is able to swap one factor input for another (slope of isoquants) Marginal rate of transformation MRT - Rate at which a firm is able to exchange production of one good (i.e. output) for another Robinson the producer: Suppose that Robinson is deciding how many coconuts to collect in order to maximise profits, taking prices as given Labour cost - w, Coconuts price - p Profit maximising condition - w = pMPL Profits (determined by iso-profit line) - Π = pY – wL

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Iso-profit line -

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Robinson maximises firm profit by producing where the iso-profit line is tangent to the

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production function: Robinson the consumer: Total endowment time - T, Coconut price - p His endowment includes his capacity for labour and profits of ‘his’ firm Budget constraint:

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Subtract wT from both sides:

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Robinson maximize his utility where: Market equilibrium is a set of prices such that: ○ Each consumer maximises utility ○ Each firm maximises profit ○ All markets clear - Supply = Demand In the Robinson Crusoe economy we need: ○ Robinson the consumer maximising utility ○ Robinson the producer maximising profits ○ Robinson the consumer wants to buy as many coconuts and work as many hours as Robinson the producer wants to sell and employ Disequilibrium: We find the firms optimum L* and Y* for some given p and w The optimal iso-profit line of the firm is also Robinson's budget constraint:

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Robinson maximize his utility given his budget constraint In this example Robinson wants to work more (L**) than the firm wants to employ him (L*). This is not market equilibrium Market equilibrium: Wage was too high (or p was too low). So might expect wage to fall (or p rise) As the wage falls the firm would want to employ more labour The consumer may or may not want to change his labour supply

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Potentially we may obtain a market equilibrium where the consumer supplies - and the producer demands - labour equal to L* Example:

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U = XY X = 24 - L...