A cruel master owns a productive slave. The master maximizes the profits he make

Question

A cruel master owns a productive slave. The master maximizes the profits he makes from selling produced only using the slave’s labor (24-L). The master does not pay the slave a wage, but he buys yams (y) for him to eat and determines the amount of leisure (L) the slave will have realizing that if the slave's utility level falls to low, he will run away and the Master's profits will fall to zero. The slave has preferences only over yams and leisure. The Master is a price taker in the markets for cotton and yams. The slave has an endowment of 24 hours to be divided between labor and leisure.

Question c) Show that the slave will be forced to work harder (receives less leisure) if the price of yams falls, and that he will receive more yams if the price of cotton rises

Question d) What will always happen if the slave requires a higher level of utility to prevent him from running away? What else can you say if his preferences are convex and homothetic.

Question e) Formulate the Master's cost minimization problem and the associated first order necessary conditions. What is the relationship between this system and the profit maximization problem?

Explanation / Answer

Master slave flip flop is basically a circit which convert level triggering into edge triggering,
there are two type of edge triggring one is positive and another is negative.positive edge triggering means output changes during a rising pulse and negative edge triggring means output chnages during falling edge.
Now if orignal master slave is positive edge trigger and by doing so as in question it becomes negtive edge trigger and if it is negative edge trigger than it will become positive edge trigger.

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