The first step is to ask what might happen to inflation. In general, whenever unemployment is lower, inflation rises more (or falls less) than it would otherwise. This would happen whether unemployment were reduced by a general reflation (with increased output) or because hours per worker had been cut (with output fixed). So what will happen if we use shorter hours to cut unemployment? Inflation will rise more than it would otherwise. Two responses are then possible.
One could say, 'Bravo! We have cut unemmployment and we are willing to accept the rising inflation." But if this is the reaction, it would obviously have been better to cut unemployment by expanding output than by simply redistributing a given amount of work over more people. So there is no case for shorter working hours along that route.
Along the alternative route the outlook is even bleaker. In this scenario the government sees inflation rising, decides it is unacceptable, and allows unemployment to rise back to its original level (so as to control inflation). The net result of shorter working hours is then no reduction in unemployment, but a reduction in output.
Which response from the government is the more likely? If shorter working hours have no effect on the trade-off between unemployment and inflation, there is no obvious reason why they should affect the mix of unemployment and inflation that the government chooses.
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