1 Robinson Crusoe Economy with Concave Production Function

In class, we assumed that Robinson receives a constant wage. This is a realistic assumption if there are no diminishing returns to his work (that is, if the amount of sh he gets for working one hour is the same regardless of the amount of hours he works). More realistically, he faces diminishing returns (that is, the more he works, the harder he gets additional sh). Imagine that his budget constraint is C = A L where L is the amount of work and C is consumption.

(a) Plot the budget constraint in the C-L space.

Imagine that Robinson's preferences are normal (that is, increasing in C, decreasing in L, and convex).

(b) Plot the indifference curve in the C-L space (Note: recall that L is labor, not leisure).

(c) Find graphically the optimal amount of work effort and consumption.

(d) Imagine that Robinson wins the lottery. That is, without having to work, he can now enjoy 10,000 sh for free. Display Robinson's new budget constraint and his new likely behavior. Make sure you explain Robinson's behavior in terms of income and substitution effects.

(e) Imagine instead that Robinson's economy experiences a positive productivity shock which is a technological improvement (that is, A in the production function increases). Plot the new budget constraint and describe the new optimal choice for Robinson. Make sure you explain Robinson's behavior in terms of income and substitution effects.

(f) What are differences between your answers in (d) and (e)? Explain.