In: Economics
Tax Incidence: How do the effects of a tax differ between markets with different elasticities of supply? Consider two hypothetical markets. In both cases, the demand function is QD = 1000 - P The two supply functions are QS1 = P - 100 and QS2 = 2P - 650
a. Solve for equilibrium price and quantity for both cases and show that the equilibrium values are the same in these two cases (for QS1 and QD and for QS2 and QD). Plot the inverse supply and demand functions (with P on the vertical axis and Q on the horizontal axis) for the two markets on the same graph. (7)
b. Now suppose a tax is imposed in both markets, equal to $100 per unit purchased. Model this as a shift in the demand curve (so that QD now depends on P, the net price paid to the firm, plus the tax). Illustrate the new demand curve on your graph (label everything clearly). Derive the new equilibrium price (the net price received by the firm) and quantity for each of the two cases. In which case is the producer’s share of the tax burden greater? (7)
c. Calculate deadweight loss in each case. In which case is deadweight loss greater? (8)
given: Qd = 1000 - P; Qs1 = P -100; Qs2 = 2P - 650
a. Equilibrium price and quantity:
for S1: 1000 - P = P - 100 or 1100 = 2P So, P = 1100/ 2 = 550 P = 550
Plugging in the value of P in demand function to calculate Q,
Qd = 1000 - P. So Q = 1000 - 550 = 450 Q = 450
for S2: 1000 - P = 2P - 650 or 1650 = 3P So, P = 1650/ 3 = 550 P = 550
Plugging in the value of P in demand function to calculate the value of Q,
Qd = 1000 - P So, Q = 1000 - 550 = 450 Q = 450
The values of price and quantity are the same for both supply functions.
Plugging in these values in the demand/ supply schedule, we get the following table:
Price | Demand | Supply 1 | Supply 2 |
0 | 1000 | - | -650 |
100 | 900 | 0 | -450 |
200 | 800 | 100 | -250 |
300 | 700 | 200 | -50 |
400 | 600 | 300 | 150 |
500 | 500 | 400 | 350 |
600 | 400 | 500 | 550 |
700 | 300 | 600 | 750 |
800 | 200 | 700 | 950 |
900 | 100 | 800 | 1150 |
1000 | 0 | 900 | 1350 |
The graph:
In the graph above, D is the demand curve, S1 is the supply curve for the first supply function (Qs = P - 100) and S2 is the supply curve for the second supply function (Qs = 2P - 650).
From the graph, we can see that equilibrium quantity = 450 units and equilibrium price = $550.
We can also see that S2 is more elastic than S1.
b. When there is tax of $100:
Graph:
The demand curve shifts to the left (blue dotted line). As a result, it intersects the two supply curves at two different points leading to two different price and quantity amounts (follow blue for S1 and pink for S2).
Ps1 = 500; Producers receive $500. Their tax burden is (550 - 500=) $50
Ps2 = 520 ; Producers receive $520. Their tax burden is (550 - 520=) $30
Between Ps1 and Ps2, tax burden is higher in case of Ps1 (supply curve - S1, which is more inelastic)
Comparing the tax burden of producers on the graph, Ps1 is farther to P than Ps2. That is producers bear more tax burden in case of S1, that is when the supply curve is more inelastic.
c. Deadweight loss for S1 = ½ * 100 * 50 (½ * tax amount * change in Q)
= 2500 DWL = $2500
Deadweight loss for S2 = ½ * 100 * 70 (½ * tax amount * change in Q)
= 3500 DWL = $3500
Deadweight loss is greater in case of S2 (when supply curve is more elastic)