Indexes, Basic Welfare Measures, Costs of Market Distortions
  1. The typical household in Berzerkistan has seen the following price changes between 1995 and 2005, and has adjusted the bundle of goods it purchases accordingly:

    ITEM P1995 P2005 Q1995 Q2005
    yurts 180 235 4 3
    yaks 150 160 5 8
    yogurts 10 20 175 125

    1. Using 1995 as the base year (1995 price index = 100) calculate the price index of the 1995 consumption bundle in 2005 prices. (This is a Lespeyres index, calculated on the ex ante consumption bundle—the way CPI is traditionally calculated)
    2. Now calculate the price index of the 2005 bundle in 2005 prices if its 1995 price index = 100. (This is a Paasche index, calculated on the ex post consumption bundle.)
    3. The typical Berzerki household had an income of 15,000 groats in 1995, and 23,000 groats in 2005. Calculate the number of 1995 consumption bundles the typical household could afford in 1995.
    4. Calculate the number of 2005 bundles it could afford in 2005.
    5. Compare the number of 1995 bundles the household could afford at 1995 prices and income versus the number of 1995 bundles it could afford at 2005 prices and income.
    6. Compare the number of 2005 bundles the household could have afforded at 1995 prices and income versus the number of 2005 bundles it can afford at 2005 prices and income.
    7. Is the typical Berzerki household better off in 2005 than it was in 1995?

  2. Suppose the inverse demand for widgets is Pd = 100 – 0.5Q and the inverse supply of widgets is Ps = 40 + 1.5Q.

    1. Graph the supply and demand. Calculate the equilibrium P and Q,and the consumer and producer surpluses.
    2. Now suppose the government imposes a $20/unit tax on widget sales. Identify the quantity at which PS = PD + $20 on the graph, and calculate the new values of Q, PS and PD.
    3. Calculate the new consumer and producer surpluses, the tax revenue and the deadweight loss generated by the tax.

  3. The US Social Security system is based on a classic sleight-of-hand tax policy first introduced in Germany by Otto von Bismarck in 1889. Germany’s Old Age and Disability Insurance Bill established a wage tax that was “pro-rated equally” between workers and employers.

    Nowadays the US government collects a 15.3% payroll tax on your gross wages: 12.4% for Social Security plus 2.9% for Medicare. These taxes are nominally split 50-50 between workers and employers, so you only see 6.2% of your gross pay withheld for SS plus 1.45% withheld for Medicare; your employer is paying matching amounts. This seems eminently fair, and these payroll taxes don’t look so bad compared to the larger IRS withholding for regular income taxes. But a simple analysis illustrates how the nominal 50:50 split of tax burden fails to account for differential bargaining powers of employers versus workers in the labor market. Where the relative wage elasticities of labor supply and demand differ, the nominal wage is shifted away from the equilibrium wage, and the burden of the tax is shared unequally.

    In this graph, the ex ante equilibrium is (W0, Q0), and a wage tax of t is introduced as a wedge between the labor demand and supply schedules. Here the elasticity of labor demand is three times greater than the elasticity of supply, so no matter how the tax is nominally apportioned between employers and workers, the reduction in workers’ take-home pay is three times greater than the increase in hourly wage cost to employers. The resulting nominal gross wage W’ will depend on the nominal allocation of the tax burden, but the hourly cost of labor for employers WD and the hourly take-home wage WS will not.

    1. Try working through a numerical example. Assume the elasticity of employer demand for labor with respect to wages is %ΔQ/%ΔWD = -1.5, the elasticity of employee supply is %ΔQ/%ΔWS = +0.5, and the ex ante equilibrium is Q0 = 100 million workers employed at an average wage W0 = WD = WS = $10 per hour.
      Now suppose the government imposes a 20% wage tax where employers pay 10% on their payrolls, and withhold 10% of gross wages from employees’ paychecks.
      Calculate the ex post equilibrium level of employment Q’, the new gross wage rate W’, the employer wage cost 1.1W’ and the take-home wage 0.9W’.
      Calculate the total tax revenue and deadweight loss generated by this tax.

    2. Now try working the reverse analysis with real numbers. With the 15.3% payroll tax in place, the US currently has about 150 million workers employed at an average reported hourly wage of about $16.80. Assume the elasticity of demand for US labor with respect to wages is -1.0, and the elasticity of labor supply with respect to wages is +0.5.
      Calculate what US employment and the average hourly wage would be in the absence of Social Security and Medicare taxes.
      Calculate the aggregate deadweight loss generated by these taxes.

  4. For over 190 years, the US has restricted imports of foreign sugar (sucrose) to “protect” the economic interests of US sugar beet and sugar cane producers. US sugar producers are not very numerous, but they are rich enough to maintain a very powerful lobby in Congress. Over the past 25 years Congress has typically restricted sugar imports to about 1 million tons per year in order to guarantee US producers a price of 22 cents per pound ($440/ton). US production is around 7 million tons per year. Annual US consumption is about 8 million tons--or 130 pounds per household. A typical world price is 6.5 cents/pound ($130/ton).

    On the graph below, S(us) represents the US producers’ supply schedule, S(world) represents world supply (assumed to be perfectly elastic) and D(us) represents US demand for sugar. Use this graph to calculate (in $) estimates of the following:

    1. The loss of consumer surplus due to the quota (area of trapezoid a-c-d-g).
    2. The excess profits accruing to foreign producers lucky enough to get a share of the US quota (area of rectangle b-c-e-f)
    3. The extra producer surplus accruing to US sugar producers (area of triangle a-b-h)
    4. The deadweight loss from the US sugar quota (area of trapezoid b-f-g-h plus triangle c-d-e)

    What effects do you think the US’s long-standing sugar import quotas have (or had) on...

    • the market value of slaves in the Louisiana Territories--a concern of sugar growers in the 1820's.
    • the Florida Everglades
    • the US candy industry
    • the artificial sweeteners industry
    • the market for US corn (source of both fructose and ethanol)
    • European Union sugar policies
    • small sugar-producing nations such as Belize and the Dominican Republic that received US food aid as compensation for being denied access to the US sugar market.
    • other sugar producers such as Colombia and Peru (what alternative crop do they export to us instead?)

    Check http://www.fff.org/freedom/0498d.asp for some detailed (but not necessarily unbiased) historical background.