Phillips Curve and Inflation Reduction: How Much Unemployment is Needed?

To calculate the unemployment rate that would reduce inflation by 4%, we need to rearrange the Phillips curve equation to solve for u:\n\nπ = π-1 - 0.4(u - 0.05)\n\nLet's assume that the current inflation rate (π) is 4%. We can substitute this value into the equation:\n\n4% = π-1 - 0.4(u - 0.05)\n\nNow, let's solve for u:\n\n4% + 0.4(u - 0.05) = π-1\n\n0.4(u - 0.05) = π-1 - 4%\n\n0.4(u - 0.05) = π-1 - 0.04\n\n0.4(u - 0.05) = π-1 - 0.04\n\n0.4(u - 0.05) = π-1 - 0.04\n\n0.4(u - 0.05) = π-1 - 0.04\n\n0.4(u - 0.05) = -0.04\n\n0.4(u - 0.05) = -0.04\n\n0.4u - 0.02 = -0.04\n\n0.4u = -0.04 + 0.02\n\n0.4u = -0.02\n\nu = -0.02/0.4\n\nu = -0.05\n\nTherefore, it would take an unemployment rate of -0.05 (or 5%) to reduce inflation by 4%.