Consider a market with a demand curve of P = 19–3q and a supply curve of P = 2q. If the government levies a tax on consumers of $4 per unit, what is the resulting DWL?

[Round your answer to two decimal places when needed]

Question

Consider a market with a demand curve of P = 19–3q and a supply curve of P = 2q. If the government levies a tax on consumers of $4 per unit, what is the resulting DWL?

[Round your answer to two decimal places when needed]

BlackTom AI · Accepted Answer

First, I will restate the given curves and the tax: Demand is P = 19 − 3q, supply is P = 2q, and there is a $4 per-unit tax on consumers. This means buyers pay Pc and sellers receive Ps with Pc = Ps + 4.
Next, find the no-tax equilibrium by setting demand equal to supply: 19 − 3q = 2q. Solving, 19 = 5q, so q* = 3.8 and the corresponding price is P* = 2q* = 7.6.
Now incorporate the consumer tax. Use the relationships: Demand uses Pc, so Pc = 19 − 3q. Supply uses Ps, so Ps = 2q. And Pc = Ps + 4 due to the tax. Substituting, 19 − 3q = 2q + 4. This gives 19 − 4 = 5q, so q_t = 3.0. Then Ps = 2q_t = 6 and Pc = Ps + 4 = 10.
Thus, with the tax the quantity traded is 3, the price buyers pay is 10, and the price sellers receive is 6.
Now compute the deadweight loss (DWL). Without tax, quantity was 3.8; with tax, it is 3. The drop in quantity is Δq = 3.8 − 3 = 0.8. For a unit tax of t = 4, the standard DWL is a triangle with base Δq and height t, so DWL = 0.5 × t × Δq = 0.5 × 4 × 0.8 = 1.6.
Therefore, the deadweight loss due to the $4 consumer tax is 1.6 (in appropriate monetary units).

BUSS1040 (ND) Quiz 3

Consider a market with a demand curve of P = 19–3q and a supply curve of P = 2q. If the government levies a tax on consumers of $4 per unit, what is the resulting DWL? [Round your answer to two decimal places when needed]

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