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Johnnie B. Linn III Concord College Athens, WV

Johnnie B. Linn III Concord College Athens, WV. Reconciling Macroeconomic And Microeconomic Approaches To Lump Sum And Proportional Taxes That Collect The Same Revenue: An Interactive Spreadsheet Approach. The Problem. Keynesian equilibrium

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Johnnie B. Linn III Concord College Athens, WV

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  1. Johnnie B. Linn IIIConcord CollegeAthens, WV

  2. Reconciling Macroeconomic And Microeconomic Approaches To Lump Sum And Proportional Taxes That Collect The Same Revenue: An Interactive Spreadsheet Approach

  3. The Problem • Keynesian equilibrium • identical impact, leaving the economy with identical levels of employment and income A T Output

  4. The Problem, Continued • Microeconomic theory of labor supply • a proportional tax reduces the opportunity cost of leisure (substitution effect) • a lump sum tax does not (no substitution effect) B S’ S C Labor   Leisure

  5. How do we Reconcile These? • Key: A change in worker productivity and a change in the work week • Why? To match output before and after a tax change • How? Change the capital/labor ratio

  6. From Lump Sum to Proportional Tax • The amount of labor offered per worker decreases. • To maintain the same level of output, employers must increase the ratio of capital to labor. • This will raise the productivity of labor and raise its after-tax wage.

  7. From Proportional to Lump Sum Tax • The households offer to work a greater number of hours per week • Too much output is produced compared to the increased amount of aggregate demand. • Employers therefore withdraw some capital from the production process, reducing the productivity of labor.

  8. How Can the Macro-Micro Reconciliation Best be Taught? • Graphical Analysis • Keynesian Cross • Aggregate Labor Demand Function • Household Labor Supply Function • Spreadsheet Analysis • Aggregate Demand Schedule • Aggregate Labor Demand • Individual Labor Supply

  9. Pros and Cons • Graphical Analysis • Well known • Good for partial equilibrium analysis • Difficult to integrate macro and micro levels • Spreadsheet Analysis • Spreadsheets not yet familiar to all • Less visual appeal • Easier to integrate macro and micro levels

  10. Our Assumptions • Fixed technology (Cobb-Douglas labor-capital production function) • Labor’s and capital’s shares of total iIncome are invariant (75% Labor, 25% Capital) • For a given level of productivity, labor and capital are hired and laid off in the same proportion. • Workweek is the same for all employed households.

  11. Assumptions, Continued • All households, whether employed or not, own equal shares of capital. • Capital is expressed in labor-equivalent units. • Each household owns 40 shares of capital. • Arguments of household’s utility function are leisure and income. • Marginal propensity to consume is imputed at macro level. • Marginal propensity to consume is constant.

  12. Assumptions, Continued • No income effect in labor supply. • Proportional tax is levied on all income, earned and unearned.

  13. The Graphical Analysis

  14. A B C G OUTPUT D E LABOR F 1. Full Employment: The Keynesian Cross and the “Sailboat”

  15. The Labor Utilization Curve (EB) • Slope of EB is the productivity of labor. • Productivity changes only if there is a change in the capital-labor ratio. • Point B is 100% employment of labor. B C G D E LABOR F

  16. The Household Income Function (DCB) • CE and BF are always in fixed proportions, so DCB is always a straight line • Slope of DCB is the wage. • Utility Function is Tangent to CB at B. B C G D E LABOR F

  17. A B P H C J M K OUTPUT D L E LABOR N HH. INCOME 2. Equilibrium at Less than Full Employment, No Taxes

  18. The Aggregate Labor Demand Function (LKJ) • Reduction in aggregate demand from A to H results in reduction of labor demand from B to J. • Demand for capital (EL) is reduced in same proportion as demand for labor (EJ). A B H C J K OUTPUT D L E LABOR

  19. The Household Labor Supply Function • Earnings of capital (EK) is divided equally among all households (NM). • Unemployed Households are at point M, employed households are at point P. B P C J M K E LABOR N HH. INCOME

  20. 3. Proportional and Lump Sum Taxes, Full Employment Case A B’ B T S’ S D R OUTPUT LABOR

  21. The Spreadsheet Approach

  22. Spreadsheet Approach: Lump-Sum Tax

  23. Lump-Sum Tax:Spreadsheet Approach (Continued) • Full employment output is $1200 • Lump-sum tax of $100 is 8.33% of GDP • Workweek is 40 hours • There are 3 households each earning $400 before taxes. • Unearned income for each household: $100. • Earned income is 40 hours @ $7.50 or $300.

  24. Lump-Sum to Proportional Tax: Spreadsheet Approach

  25. Lump-Sum to Proportional Tax:Spreadsheet Approach (Continued) • Equilibrium output is $1200. • Proportional Tax is 8.33% or $100 • The household labor market is not in equilibrium • The after-tax wage is $6.88. • Households offer to work 36.67 hours, or 8.33% less than before. • Employers still want a 40-hour workweek.

  26. Lump-Sum to Proportional Tax: Employer Reaction • A 10% boost in output is needed to meet demand. • Part of this can be met by raising worker productivity. • Increased productivity means higher after-tax wage. • Higher after-tax wage will boost hours offered per week and meet remainder of output target.

  27. Lump-Sum to Proportional Tax:Employer Reaction (Continued) • Try a 5% increase in productivity. • Productivity will be raised from 10.0 to 10.5 (part of this can be attained immediately because some surplus capital is initially available). • An eventual increase in the capital base from 120 to 139 will be needed. • Workers will be constrained to working more hours than they would like until the capital base is built up. • Split the Difference on the Workweek. • Midpoint of spread is 38.33 hours.

  28. Proportional Tax: First Iteration

  29. Result of First Iteration • The 5% productivity boost has overshot its target slightly. • The before-tax wage is $7.88. • The after-tax wage is $7.22. • The workweek desired by employers is 38.33 hours. • The workweek offered by labor is 38.50 hours, a .17 hour surplus. • The next iteration should be a small negative change in productivity and a small increase in the workweek.

  30. Proportional Tax: Solution

  31. Final Figures • Productivity is 10.44 • Before-tax wage is $7.83. • After-tax wage is $7.18. • Workweek is 38.3 hours. • Capital base is 137.

  32. Proportional Tax to Lump-Sum Tax • Labor desires a workweek that is too long. • Employers will reduce the amount of capital applied to labor. • Lower productivity will reduce drag of too much output. • Lower wage will shorten workweek and eliminate remainder of drag on output. • Change can be rapid because there is surplus capital.

  33. Reprise • Graphical Approach: • Compact. • Individual components can be studied in isolation. • Process is less transparent. • Spreadsheet Approach: • Less compact. • Process is more transparent.

  34. We now return you to your regular programming.

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