Suppose that both consumption and leisure are always normal goods. Keep in mind the underlying cause for deadweight losses from wage-distoring taxation as you answer the questions below.
A: Explain why the following either cannot happen or, if you think it can happen, how:
(a) Labor supply is perfectly vertical but there is a significant dead weight loss from taxing wages.
(b) Labor supply is perfectly vertical and there is no dead weight loss from taxing wages.
(c) Labor supply is downward sloping and there is a deadweight loss from taxation of wages.
(d) Labor supply is upward sloping and there is a deadweight loss from taxing wages.
(e) Labor supply is downward sloping and there is no deadweight loss from taxing wages.
(f) Labor supply is upward sloping and there is no deadweight loss from taxing wages.
B: Now suppose that tastes can be summarized by the CES utility u(c, ℓ) = (0.5c−ρ + 0.5ℓ−ρ) −1/ρ, where c is consumption and ℓ is leisure.
(a) Are there values for ρ that would result in the scenario in A (a)
(b) Are there values for ρ that would result in the scenario in A (b)?
(c) Are there values for ρ that would result in the scenario in A (c)?
(d) Are there values for ρ that would result in the scenario in A (d)?
(e) Are there values for ρ that would result in the scenario in A (e) and A (f)?