Hi Tunc,

I think the answer will be different for every gene. If each copy of the gene is a perfect copy, and has its own intact promoter, then you might expect expression levels of the protein to scale linearly with the copy number. But, most genes have some sort of negative-feedback loop controlling their expression. So the more of the transcript (or protein) that exists in the cell, the less new transcription occurs. Or transcription occurs, but more transcripts are degraded before being translated. Or more translation occurs but more of the proteins are digested and recycled. There are many levels and mechanisms for controlling protein levels, so I suspect that for many genes  an increased copy number will not always increase apparent expression levels.

And if the duplication of those genes occured enough generations ago, whilst they might appear to be perfect copies in the coding sequence there may be crucial mutations occuring in the promoters and other control regions, that mean they do not all get switched on/off at the same time or by the same conditions. Having multiple copies of a gene allows the propagation of these mutations in some of them whilst preserving the function of the original.

there are genes that are generally located on chromosomal regions that are constitutively silent. So, copy number of a gene does not always correlate with higher gene expression. 

the expression of desired gene integrated chromosomally attributes to many factors, not only the copy number, but the locus position for integrating foreign genes in the chromosome and several factors, including transcription rates, mRNA stabilities, and translation rates.

Copy numbers of a gene does not always leads to increase the gene expression as there are some genes located on chromosomal regions that are constitutively silent.