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Question: consider a oneperiod economy there is a household that is...

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Labor taxation: The The Laffer Curve Consider a one-period economy. There is a household that is endowed with one unit of labor and the following preferences over consumption c and leisure 1-1: 1- Y (1 where 0 and Y 0.1 The government has to finance a given level G 0 of expenditure; it can do this by levying a proportional tax T on labor. There is also a representative firm with technology y Ald, where la is labor demand and A G> 0. Markets for the consumption good and for labor are competitive. 1. Planners problem: Finding the efficient allocation. (a) Write down the planners problem for this economy (b) Find the first-order condition (FOC) for the planners labor choice and interpret it briefly. (c) Find the efficient allocation. 2. Competitive equilibrium: (a) Firms problem: What must the gross wage w and the net wage w be in equilibrium (no calculation necessary (b) Households problem: i. Write down the households problem. ii. Find the FOC for labor. Interpret and compare to the FOC in e planners problem. iii. Show that optimal labor supply is given by 1/Y w(1 -T) 1 +n How does labor supply react to a tax increase for different values of Explain briefly the mechanism behind your result. 1 we obtain the log-preferences ln c +nln(1 Recall that for iv. From now on, use the parameter values A 2 and 0.7. Use a spreadsheet program to plot the Laffer curve, i e. tax revenue of the government as a function of T. Explain. (c) Government: Write down the governments budget constraint. (d) Equilibrium i. Define a competitive equilibrium for this economy. ii. What is the maximum level of G that can be supported in equi- librium (again, use A 1, n 2 and 0.7)? iii. Suppose now that G 0.1 (and A 1, n 2, Y 0.7). What are the equilibrium prices and ?3 Which policy would allocations you recommend to the government iv. In general, can the government implement the efficient allocation by any labor tax T? Argue why (not). What if the government had the possibility to use lump-sum taxation?

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