Labor Migration and Urban Unemployment: Reply
I would like to thank Paul Zarembka for pointing out what is apparently a very careless mathematical error in my paper. In actual fact, however, my carelessness was not so much a failure to make a correct algebraic substitution as a failure to explain briefly why I changed the form of my analytical equilibrium model equation (8) from that directly implied by the underlying behavioural model-i.e. why I did not use Zarembka's equation (8a). The model set forth in my paper represented an attempt to provide a concise and mathematically rigorous formulation of a phenomenon which was described verbally, in considerably more detail, in an earlier paper published in the Yale Economic Essays. Unfortunately, in my desire to be concise I carelessly forgot to point out in the sentence before equation (8) that for analytic as well as policy purposes I was separating the employment probability variable, 7r(t), from the percentage urbanrural wage differential variable, a(t), so that each could be treated independently-i.e., the sentence should have read, Next we specify an aggregate labor supply equation which is a simplified version of equation (1) in the sense that only a one-period time horizon is assumed and the probability variable ('r) for analytical and policy purposes is treated separately from the wage differential variable. Now, having expressed my mea culpa for this carelessness, let me turn to Zarembka's correction and show why he also has been very careless in greatly exaggerating the quantitative significance of my apparent mathematical error. I shall then show why I feel that my equation (8) is a much better way of formulating the labor supply function than is Zarembka's (8a). Briefly, Zarembka shows that if I had made the proper substitution in equation (8) on the basis of my earlier equations (2) and (3), then my equilibrium employment rate could be closely approximated by
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