How does cost-push inflation affect the Phillips Curve relationship between inflation and unemployment?

Cost-push inflation occurs when the costs of production for businesses rise, leading them to increase prices for consumers. This type of inflation can shift the Phillips Curve, which originally suggests that lower unemployment comes with higher inflation. When costs rise, businesses may reduce their workforce to manage expenses, causing unemployment to increase even as inflation rises. For example, if the price of oil skyrockets, transportation and manufacturing costs go up, leading to higher prices for goods and potentially more layoffs. This means that instead of the usual trade-off where lower unemployment leads to higher inflation, both inflation and unemployment can rise together, complicating economic policy.