How do you do the algebra to get the equation in the blue bracket? and what does the b with a hat thing like mean? please give detailed explanations , thank you!

To solve the model, we first note that the flexible wage is set according to the wage-setting rule above: AW AW: - b(us - u") . But what about the rigid wage? To find it, we need to realize one thing: the increase in the rigid wage will be set equal to the expected average wage increase as seen from the end of the previous year: AW AW WHI WE This is shown formally in the appendix to this chapter, but the result can be explained intuitively. The expected wage level is a weighted average of the rigid wage and the expected flexible wage. If the expected wage level was higher than the rigid wage, this would mean that the expected flexible wage would be higher than the rigid wage. But since the flexible wage is set optimally, based on actual con- ditions, there would be an incentive for the rigid-wage firms to raise their wages. Therefore, it can never be optimal for rigid-wage firms to set a wage below the 2 expected average wage level. Substituting the equations above for the flexible and the rigid wage into the equation for the average wage change we get AW. [AW: - blue - u") + (1-2) Aw; Now we can solve for the average wage change to get AW. Wi - b(u , - 2" ) where be 1- 2