Production with Constant Returns

This chapter examines the net supply correspondence of a constant returns to scale firms under suitable convexity and smoothness assumptions. These assumptions are comparable to those used in the previous chapters for consumers and production with decreasing returns to scale. The chapter starts by formulating constant returns to scale production by way of production sets with arbitrary numbers of inputs and outputs. It then addresses the profit maximization problem of a constant returns to scale firm. That problem does not always have a solution. More accurately, if some feasible activity yields a strictly positive profit at some given prices, then it suffices to consider an arbitrarily large multiple of that activity vector to get a feasible activity that yields an arbitrarily large profit at the same prices. The firm can then make an arbitrarily large profit.

The Big-Five Factors of Personality: Possible Structure, but No Consensus within the Structure

Preliminary analysis of Goldberg's clustered adjectives and data from Activity Vector Analysis suggest five factors but some differences.

Probabilistic analysis of a learning matrix

A learning matrix is defined by a set of input and output pattern vectors. The entries in these vectors are zeros and ones. The matrix is the maximum of the outer products of the input and output pattern vectors. The entries in the matrix are also zeros and ones. The product of this matrix with a selected input pattern vector defines an activity vector. It is shown that when the patterns are taken to be random, then there are central limit and large deviation theorems for the activity vector. They give conditions for when the activity vector may be used to reconstruct the output pattern vector corresponding to the selected input pattern vector.

Probabilistic analysis of a learning matrix

A learning matrix is defined by a set of input and output pattern vectors. The entries in these vectors are zeros and ones. The matrix is the maximum of the outer products of the input and output pattern vectors. The entries in the matrix are also zeros and ones. The product of this matrix with a selected input pattern vector defines an activity vector. It is shown that when the patterns are taken to be random, then there are central limit and large deviation theorems for the activity vector. They give conditions for when the activity vector may be used to reconstruct the output pattern vector corresponding to the selected input pattern vector.