Assume That the Production Function for an Economy Is Given

question 9

Essay

Assume that the production function for an economy is given by Y = AK^aH^bL^1-a-b,where H is the stock of inventories.Then the marginal product of inventories (MPH)is given by MPH = bAK^aL^1-a-bH^b-1.If the stock of inventories does not depreciate,the price of inventories is the same as the price of output,and taxes are ignored,then the real "cost of capital" for inventories is just the interest rate r.a.Derive an expression for the "desired equilibrium stock of inventories" (H*)as a function of r and output Y by equating the cost of capital to MPH. (Hint: First substitute the production function into the expression for MPH to get MPH = bY/H.)If r = 0.1,b = 0.05,and Y = 5,000,what is the desired stock of inventories?
b.If r rose to 0.12,how would the desired stock of inventories change?

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Definitions:

Life Span

The maximum duration of life of a living organism or the period from birth to death, considering all factors affecting its life cycle.

Developmental Theory

A framework for understanding how and why people change or remain the same over the course of their lives.

High Level

Describes processes, concepts, or activities that are advanced in complexity, abstraction, or general importance.

Operant

An accidental or random action.