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Q2. The slope of the Phillips curve. The text presents several closely related versions of the Phillips curve. (a) The first version of the Phillips curve relates wage inflation to unemployment: WII WI-1 -b(u,-u") the slope of this Phillips curve is given by b=Ab/(1-2). Give an intuitive interpretation of the formula for the slope, explaining both what A and b represent, as well as how they affect the slope. In the textbook model, A represents the fraction of firms who can change their wages in a given year, and this is meant to proxy for the degree of wage flexibility in the economy. When A is high, the Phillips curve is steep, and small changes in unemployment can have large effects on wage inflation. When A is small, much larger changes in unemployment are required to have the same effect on inflation. b represents the strength of the (negative) relationship between unemployment and changes in the firm's desired wages. The formula (from an earlier chapter) is: % Adesired wage =% Aaverage wage-b (u, -u" ) So that when b is large, firms want to cut wages by a lot in times of high unemployment, and when b is small, firms only desire small wage cuts when unemployment is high. As for the effect on the Phillips curve, the curve is steeper when b is large (i.e. when desired wages are highly responsive to the unemployment rate, then small changes in unemployment can have relatively large effects on wage inflation). i. Calculate the slope of the Phillips curve if b=1 and 1=1/2. b= Ab _(1/2) x 1 =1 1-1 1/2 ii. Calculate the slope of the Phillips curve if b=1 and 1=1/3. Contrast with (a - i). 6= Ab _(1/3) x 1 2/3 =0.5 When there is less wage flexibility, the Phillips curve becomes flatter. iii. Calculate the slope of the Phillips curve if b=2 and 1=1/2. Contrast with (a - i). b=Ab -=(1/2) x26-6 =2 1- 2 1/2When the desired wage is more responsive to the unemployment rate, the Phillips curve becomes steeper. (b) The third version of the Phillips curve relates inflation to output: n= n + BY+z the slope of this Phillips curve is given by B=b x Y"/ EL. Give an intuitive interpretation of the new terms that have appeared in the Phillips curve and in the slope term since part (a). This version of the PC replaces the expected average wage change with a term for expected inflation It , it is written in terms of the output gap Y =(Y-Y")/ Y" instead of the earlier version which was based on a measure of excess unemployment, and there is now a cost- push shock Z which represents deviations of productivity growth from trend. The slope of the Phillips curve - B - is now scaled by Y"/ EL which is the ratio of the natural level of output to the level of output that would prevail if the entire labour force were employed. But b remains within B, and so the slope term behaves broadly as it did before. i. Assume the natural rate of unemployment is 5% and the production function is Y = EN. Calculate the slope of the Phillips curve if b=1 and 1=1/2. Contrast this with your answer from part (a - i). EL B=by_EN"_E 1-0.05 Lb x 0.95 EL EL B=0.95 x Ab =0.95 x (1/2) x 1 1 - 2 = 0.95 1/2 Now that we take account of unemployment, the slope is 5% flatter. ii. Assuming the same production function as above, calculate the slope of the Phillips curve if b=1 and 1=1/3. Contrast with (a - ii). B=0.95 x - =0.95 x (1/3) x 1 1 - 2 =0.475 2/3 Now that we take account of unemployment, the slope is 5% flatter. iii. Calculate the slope of the Phillips curve if b=2 and 1=1/2. Contrast with (a - iii). B=0.95 x Ab 1 - X =0.95 x (1/2) x267= 1.9 1/2 Now that we take account of unemployment, the slope is 5% flatter