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I was doing some reading on Lucas' islands model and how aggregate supply can change depending on agent's expectations regarding monetary policy.

It's always assumed that there are "n" isolated islands and "n" agents producing output all by themselves. There are no firms in this setting and output supplied depends on (pi/p) with pi is price of the product producer receives and p is the general price level.

I want to assume in a situation which instead of individuals producing by themselves, firms exist and they produce output and hire labor according to the point where their marginal cost equals their marginal supply (which indicates perfect competition).

Let's suppose nominal money supply double with general price level being doubled but the demand for the firm's product is unchanged due to consumers' preferences. Although nominal monetary amount of profit would not change, the inflation-adjusted amount of profit would decrase by half.

Here's where I'm having a confusion, I presume a decrease by half in firm's inflation adjusted profits would cause firm's owner to decrase production, thus a shift of supply curve to the left. I'm making this assumption by assuming firm's owner also have a utility function where real profits induce firm's owner to spend less time running the firm, because leisure is more prefable now.

I'm unable to come across this type of a situation searching through the papers.

Are my assumptions correct?

Thanks in advance.

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