1 The government is considering taxing the production of wid

1. The government is considering taxing the production of widgets and wants to understand the distributional consequences. In response to your request for more information, your research assistant reports back to you that: • The long-run demand curve for widgets is approximately linear with a slope of 1.0, so that a $1 increase in the price causes a one-unit reduction in quantity demanded. • The short-run demand curve for widgets is approximately linear with a slope of 2.0, so that a $2 increase in the price causes a one-unit reduction in quantity demanded. • The only input into the production of widgets is labor (widget makers). • The short-run supply curve of labor into the widget industry is approximately linear with a slope of 1.0. • In the long-run, would-be widget makers have many other equally-attractive opportunities. (a) In the short run, what fraction of the tax is borne by consumers of widgets? What fraction is borne by workers in the widget industry? What is the intuition for this result? (b) In the long run, what fraction of the tax is borne by consumers of widgets? What fraction is borne by workers in the widget industry? What is the intuition for this result? (c) What is the deadweight loss from a $3 per-widget tax in the short run? And in the long run? What is the intuition for this result?

Solution

(a) In the short run,

Fraction of tax borne by consumers = 1 / (1 + 2) = 1/3 = 0.33

Fraction of tax borne by workers = 2 / (1 + 2) = 2/3 = 0.67

The reason is, absolute elasticity of consumer demand curve is 2, but absolute elasticity of labor supply curve is 1, so consumer demand is double more elastic than the supply curve. Hence, consumers bear one-half of tax burden than the tax burden shared by workers.

(b)

In the long run, both consumers & workers share 50% of the tax burden each, because absolute value of elasticity of demand and labor supply is equal.

(c)

Deadweight loss cannot be computed unless exact forms of consumer demand and labor supply curves are provided.