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We estimate the relationship between firms’ production flexibility and profitability under extreme positive demand shocks using the European toilet paper manufacturing industry in 2020 as a case study. This industry faced extreme increases in demand due to consumers panic purchasing toilet paper after the outbreak of the COVID-19 pandemic. Our estimates show that flexibility and profitability are positively related. This is even more pronounced in times of an extreme positive demand shock when a ten percent improvement in flexibility is associated with a five percent increase in profitability.