I. The Robinson Crusoe Economy
Plays a dual position: as customer and as manufacturer.
He chooses among two products: leisure and coconuts as a customer. If perhaps he sits on the seaside watching the ocean, he can consuming leisure. If this individual spends his time gathering coconuts, he has a fraction of the time for leisure but reaches eat the coconuts. We can depict Brown production opportunities and personal preferences over the two goods.
At this point, the slope of the not caring curve must equal the slope ofthe production function by the regular argument: if they entered, therewould always be some other feasible point that was recommended.
The utility making the most of choice to get Robinson has to be the point at which the greatest indiп¬Ђerence contour just touches the production function. Why? At any time inside the development function, Robinson could pick a diп¬Ђerent point that involved less labor and/or even more coconuts. Considering that he likes to be on larger indiп¬Ђerence curves, he will need to choose the top one that may be possible. This means a great indiп¬Ђerence competition that just touches the production function. Presuming the production function and the indiп¬Ђerence curves are both diп¬ЂerВ¬entiable at this point, we can consider that with the optimum choices for labor and coconuts, the marginal item of labor equals the marginal rate of replacement between leisure time and coconuts. This makes impression. The minor product of labor is the extra volume of coconuts Robinson would get from quitting one unit of enjoyment. The MRS is the little utility gets from coconuts per product of minor utility by leisure. Therefore , imagine that initially the MRS waw more than the MEGA-PIXEL. Then think about what happens in the event Robinson consumes one significantly less hour gathering coconuts. His consumption of coconuts falls by the MP of labor. His power from enjoyment goes up by marginal power of leisure. His electricity from coconuts goes down by the marginal power of coconuts divided by the marginal energy of enjoyment. Under the assumption that the MRS initially is greater than the MEGA-PIXEL, this causes a net increase in energy, so the initial choice of labor and coconuts could not have been completely optimal. 2. Crusoe Inc.
So far we have viewed Robinson problem in a way that takes into account both his manufacturer role fantastic consumer part. Now a few think about what happens if Brown decides to alternate between his two jobs. One day this individual behaves like a producer, as the next day he behaves being a consumer. Suppose Robinson creates a labor market and a coconut market. Robinson also provides an impressive п¬Ѓrm, which usually he is the owner of. The п¬Ѓrms uses labor to gather coconuts, which it sells inside the coconut marketplace. The п¬Ѓrm will consider the prices intended for labor and coconuts and after that decide how very much labor to use and how various coconuts to produce. The п¬Ѓrm's decisions will probably be determined by proп¬Ѓt maximization. Robinson, as a employee, earns pay from the п¬Ѓrm. Robinson, because the owner of the п¬Ѓrm, gets proп¬Ѓts. Johnson, as a customer, decides simply how much of the п¬Ѓrm's output to purobinsonhase. To keep track of these orders, Robinson invents a foreign currency, called us dollars. Assume that we all set the buying price of coconuts at $1 an item; that is, we all make coconuts the numeraire. This means all of us only need to decide the income rate. All of us will think about this from the point of view of the п¬Ѓrm (Crusoe, Inc. ), and after that from the point of view the consumer (Robinson). Speciп¬Ѓcally, we would like to derive the equilibria in the markets for labor and coconuts.
III. The Firm
Every evening, Crusoe, Inc. determines how much labor it really wants to hire thenext day, and exactly how many coconuts it would like to produce. Offered a price ofcoconuts of 1 and a wage rate of labor of w, we are able to solve the firm'sprofit maximizationproblem in Physique 32. installment payments on your We initial consider almost all combinationsof coconuts and labor that deliver a constant degree of profits, ПЂ. This meansthat
ПЂ = C в€’ wL.
Fixing for C, we have
C = ПЂ + wL.
Just as in Section 19, this formula explains the isoprofit linesвЂ”all combinations of labor and coconuts...