Question

Include correctly labeled diagrams, if useful or required, in explaining your answers. A correctly labeled diagram must have all axes and curves clearly labeled and must show directional changes. If the question prompts you to “Calculate,” you must show how you arrived at your final answer.


Assume the market for good Y is in equilibrium.

(a) Draw a correctly labeled demand and supply graph for good Y. Label the equilibrium price
and the equilibrium quantity
.

(b) Assume the government imposes a per-unit tax on good Y. On your graph in part (a), show each of the following after the tax has been implemented.

(i) The equilibrium price labeled
and the equilibrium quantity labeled

(ii) The area representing the change in consumer surplus, shaded completely

(c) Will the price paid by consumers increase by the same amount as the tax? Explain.

(d) Will the loss in consumer and producer surplus be greater than, less than, or equal to the tax revenue collected by the government? Explain.

Answer 1

(a) Initial equilibrium — correctly labeled demand & supply graph

Price (P)
^
| D
| \
| \
| \
| \
| \
| \ S
| \ /
| \ /
| \ /
| \ /
|----------------------X------------------> Quantity (Q)
Q_e

Labels:
- Downward sloping curve: D (demand)
- Upward sloping curve: S (supply)
- Intersection X is the initial equilibrium:
- Equilibrium price: P_e (label that on the vertical axis level of X)
- Equilibrium quantity: Q_e (label that on the horizontal axis at X)

(b) Per-unit tax on good Y

A per-unit tax t can be represented as a parallel upward shift of the supply curve by the amount t (if the tax is levied on sellers). The new supply curve is S + t. The new intersection with demand determines the new quantity and the price paid by consumers.

Diagram with tax (shaded areas use X to indicate the change in consumer surplus — see explanation below):

Price (P)
^
| D
| \
| \
| \
| \
| \
| \ S + t
| \ /
| \ /
| \ /
| \ /
| \ /
|-----------------------\---------/--X <-- intersection of D and S+t (consumer price P_c)
| \ /
| \ /
| \ /
| \ / S <-- original supply
|---------------------------X------------------> Quantity (Q)
Q_t Q_e

Labels and notation:
- Original equilibrium: at X where D intersects S:
- Price = P_e
- Quantity = Q_e
- After the tax:
- New supply: S + t (upward shifted supply)
- New equilibrium quantity = Q_t (Q_t < Q_e)
- Price paid by consumers = P_c (the vertical coordinate of intersection of D and S + t)
- Price received by producers = P_p = P_c - t (the level on the original S curve at Q_t)

(b)(i) On the graph above:
- Label the new equilibrium price paid by consumers P_c at the intersection of D and S + t.
- Label the new equilibrium quantity Q_t on the horizontal axis beneath that intersection.

(b)(ii) Area representing the change in consumer surplus — shaded completely

Consumer surplus decreases for two reasons:
1. Consumers pay a higher price on the units still bought: loss = (P_c − P_e) × Q_t (a rectangle).
2. Consumers buy fewer units: loss = area under demand above P_e between Q_t and Q_e (a triangle).

On the diagram above, the total change (loss) in consumer surplus is the sum of those two shaded regions:
- Rectangle from Q = 0 to Q = Q_t between prices P_e and P_c (shade this completely with X).
- Triangle between Q_t and Q_e under the demand curve and above P_e (shade this completely with X).

(If you redraw the picture, shade those two regions entirely to indicate the full loss of consumer surplus.)

(c) Will the price paid by consumers increase by the same amount as the tax? Explain.

No — in general the price paid by consumers (P_c − P_e) will not equal the full tax amount t. The tax burden is shared between consumers and producers; how it is split depends on the relative price elasticities of demand and supply:

- If demand is relatively more inelastic (steeper) than supply, consumers bear a larger share of the tax (P_c − P_e large).
- If supply is relatively more inelastic (steeper) than demand, producers bear a larger share of the tax (P_e − P_p large).
- Only in special cases does the consumer price rise by the full tax: for example, if supply is perfectly inelastic (vertical), producers cannot reduce quantity, so consumers pay the entire tax; similarly, if demand is perfectly inelastic (vertical), consumers also pay the entire tax. If supply is perfectly elastic (horizontal), producers bear the entire tax and consumer price does not rise.

Intuition: the incidence of a per-unit tax does not depend on whether it is legally imposed on buyers or sellers — it depends on relative elasticities.

(d) Will the loss in consumer and producer surplus be greater than, less than, or equal to the tax revenue collected by the government? Explain.

The combined loss in consumer plus producer surplus is greater than the tax revenue collected by the government. Reason:

- Tax revenue = t × Q_t (a rectangle of height t and width Q_t).
- The total reduction in surplus (consumer loss + producer loss) equals tax revenue plus an extra loss called deadweight loss (DWL), which arises because trade falls from Q_e to Q_t. The DWL is the sum of the two small triangles between the demand and supply curves over the interval (Q_t, Q_e). These triangles represent mutually beneficial trades that no longer occur because of the tax.

So:
- Consumer surplus loss + Producer surplus loss = Tax revenue + Deadweight loss.
- Therefore combined surplus loss > Tax revenue, except in degenerate cases (e.g., perfectly inelastic supply or demand) where the DWL is zero and combined loss equals tax revenue.

Summary of special cases:
- If demand or supply is perfectly inelastic, DWL = 0, and the combined loss equals tax revenue (the burden falls entirely on one side).
- Otherwise, DWL > 0 and combined loss > tax revenue.