Question

Answer 1

| P-100- (T/3) | Q-200- (2T/3) | TR-PQ | TR in thousands 10 16.2 9.8 100 180 140 100 10000 16200 9800 5000 1800 200 0 100 30 70 150 210 270 300 1.8 0.2 30 10 0 20 0

New equilibrium is where; Demand after tax = Supply

300 - (P + T) = 2P

300 - P - T = 2P

300 - T = 3P

P = (300 - T)/3

P = 100 - T/3

At Q = 200 - 2T/3, price at which this quantity intersects demand curve;

Qd = 300 - P

200 - 2T/3 = 300 - P

P = 300 - 200 + 2T/3

P = 100 + 2T/3

Base of triangle is [(100 + 2T/3) - (100 - T/3)] = 100 + 2T/3 - 100 + T/3 = T

Height is 200 - 200 + 2T/3 = 2T/3

DWL = 1/2 x base x height = 1/2 x T x 2T/3 = T²/3

Deadweight Loss 00 90 0 150 80 210 240 270 300

The government could decrease dead-weight loss by reducing the tax.

The government could increase tax revenue by reducing the tax to $ 150.

Answer 2

a.

Because tax revenue is equal to T×Q$\mathit{T}\times \mathit{Q}$ and Q=200−2T3$\mathit{Q}=200-\frac{2\mathit{T}}{3}$, you can compute tax revenue as a function of T$\mathit{T}$ in the following way:

Tax Revenue$\mathit{Tax Revenue}$	= $\mathit{ }=\mathit{ }$	T×Q$\mathit{T}\times \mathit{Q}$
	= $\mathit{ }=\mathit{ }$	T×(200−2T3)$\mathit{T}\times \left(200-\frac{2\mathit{T}}{3}\right)$
	= $\mathit{ }=\mathit{ }$	200T−2T23$200\mathit{T}-\frac{2{\mathit{T}}^2}{3}$

Plugging in tax values of $0, $30, $90, $150, $210, $270, and $300, yields a tax revenue of $0, $5,400, $12,600, $15,000, $12,600, $5,400, and $0 respectively. See Section: Deadweight Loss and Tax Revenue as Taxes Vary.

b. 

Recall that the area of a triangle is 12×Base×Height$\frac{1}{2}\times \mathit{Base}\times \mathit{Height}$.

According to this graph, the base of the deadweight loss triangle isT$\mathit{T}$   , and the height is2T3$\frac{2\mathit{T}}{3}$   .

c.

The area of the triangle that represents the deadweight loss is 12×Base×Height$\frac{1}{2}\times \mathit{Base}\times \mathit{Height}$, where the base is the change in the price (which is the size of the tax) and the height is the amount of the decline in quantity (200−(200−2T3)$200-\left(200-\frac{2\mathit{T}}{3}\right)$). Therefore, you can compute deadweight loss as a function of T$\mathit{T}$ in the following way:

Deadweight Loss$\mathit{Deadweight Loss}$	= $\mathit{ }=\mathit{ }$	12×Base×Height$\frac{1}{2}\times \mathit{Base}\times \mathit{Height}$
	= $\mathit{ }=\mathit{ }$	12×T×2T3$\frac{1}{2}\times \mathit{T}\times \frac{2\mathit{T}}{3}$
	= $\mathit{ }=\mathit{ }$	T23$\frac{{\mathit{T}}^2}{3}$

Plugging in tax values of $0, $90, $180, $240, and $300 yields deadweight losses of $0, $2,700, $10,800, $19,200, and $30,000, respectively. See Section: Deadweight Loss and Tax Revenue as Taxes Vary.

d.

The government now levies a tax on this good of $200 per unit.

Which of the following statements are true? Check all that apply.

The government could decrease deadweight loss by reducing the tax.

The government could increase tax revenue by reducing the tax to $150.