4. Consider the ASAD model of a closed economy with zero ongoing inflation and workers misperceptions. Firms are perfectly competitive, produce output with diminishing marginal returns to labour and have perfect foresight over the price level. Workers, instead, expect zero inflation in each period. At time zero, the economy is in the potential equilibrium. There is a negative shock on aggregate demand – for example, a permanent fall in desired autonomous consumption at time t = 1. What are the effects of the shock on the equilibrium real wage in the short and in the medium run? Describe (at least in words, and even better in a diagram) the entire time path of the real wage from before the shock to the medium-run equilibrium. Prove your statements formally – for example, use the diagram of the labour market where you measure the real wage on the vertical axis, and distinguish the very short run (the temporary equilibrium at time t = 1) from the medium run. Carefully explain the economic intuition for your results and add any comment you may have about the cyclicality of real wages during recessions.

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Hint: to solve this exercise, you can manipulate the equation for labour supply

W_(t) = P_(t-1) b N_(t)

where W_(t) is the nominal wage requested in period t, P_(t-1) is the past price level of period t - 1 that workers expect to prevail in the market in period t, the slope coefficient b is a positive constant, and N_(t) is work supplied.

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