We are going to test what our simple model would tell us and relate this back to data. First let's see what our model tells us: Questions 1. Assume that labor markets clear, i.e. that the labor supplied is equal to the labor demanded at the equilibrium wage rate w. Using the consumption-leisure optimality condition and the firm's wage bill obtained from your answer above, show how the hours worked is a function of the labor income tax, the ratio of consumption to output and parameters of the model. You should not have the wage rate show up in your answer. 2. Assume 0 < a < 1,γ > 0 and 0 <τₙ,<1. Are hours worked increasing or decreasing in the labor income tax? 3. We want to see how well the model performs against data. To do this, we will replicate Prescott's exercise and update the numbers using more recent data! (a) First, download the file consgdp.xls from the project folder on Blackboard. Find the con- sumption to output (GDP) ratio ₜ , ,, for each period between 2000 - 2013. Report the average consumption to output ratio for each country for the period 2000 - 2013.
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Country In Germany 0.59 France 0.59 Japan 0.37 U.K. 0.44 U.S. 0.40 s
(b) Use the following labor income tax rates for each country. Calculate the model predicted weekly hours worked in each country using the equation derived above and the average ᶜ — ᵗ calculated in your answer above. In calculating your answer, assume a=0.33, γ= 1.54 and h=100. (c) Now download the file hours.xls from the project folder on Blackboard. Report the aver- age weekly hours for each country over the period 2000-2013. (d) How does your answer above compare to the model predicted average hours?"