Per-Unit Subsidy Lab: Compare Prices and Output
Change linear supply and demand and a seller subsidy. Compare buyer and seller gains, government cost, and deadweight loss.
Free, with no sign-up.
For High school students and adults reviewing the topic.
About 8 minutes.
How does it work?
- Change a control to update the table and diagram.
- Open a preset to compare settings, then try the challenges.
What will you get?
Compare the model’s outputs, explore its presets, and check two challenges.
What does the model assume?
- Demand is Pb = A − bQ and supply is Ps = C + dQ. The controls specify A, b, C, and d in these inverse curves.
- The per-unit subsidy s is paid to sellers, so Ps = Pb + s. Equilibrium satisfies A − bQ + s = C + dQ.
- The market is competitive. Private costs and benefits equal social costs and benefits; there are no externalities or other market failures.
- Government cost is sQ. Deadweight loss is half of s times the increase in quantity beyond the unsubsidized equilibrium.
- The comparison neglects administration and the cost of raising public funds. Curves are fixed, and all quantities and prices are illustrative for one period.
- A steeper inverse demand curve is less responsive to price at a given point. The controls keep quantities and prices positive.
Which setup would you like to try?
What can you change?
Range: 100 to 200 dollars/unit.
Range: 0.5 to 5 dollars/unit².
Range: 20 to 80 dollars/unit.
Range: 0.5 to 5 dollars/unit².
Range: 0 to 20 dollars/unit.
What does the model predict?
| Quantity | Value | Unit |
|---|---|---|
| Quantity before subsidy | 25.00 | units |
| Price before subsidy | 70.00 | dollars/unit |
| Quantity after subsidy | 28.00 | units |
| Price buyers pay | 64.00 | dollars/unit |
| Price sellers receive | 76.00 | dollars/unit |
| Buyer gain per unit | 6.00 | dollars/unit |
| Seller gain per unit | 6.00 | dollars/unit |
| Buyer share of subsidy | 50.0 | % |
| Seller share of subsidy | 50.0 | % |
| Government cost | 336.00 | dollars |
| Deadweight loss | 18.00 | dollars |
Solid: demand. Long dashes: supply. Dots: supply minus subsidy. Diagonal hatching: government cost. Crosshatching: deadweight loss.
Quantity rises from 25 to 28. Buyers pay 64 and sellers receive 76 dollars per unit. Government cost is 336 dollars and deadweight loss is 18 dollars.
Can you reach these targets?
Keep a 12-dollar subsidy and a supply slope of 1. Choose a demand slope so buyers receive 80% of the subsidy.
- Target: Seller subsidy per unit = 12 dollars/unit; tolerance 0 dollars/unit.
- Target: Supply slope = 1 dollars/unit²; tolerance 0 dollars/unit².
- Target: Buyer share of subsidy = 80 %; tolerance 0.01 %.
Use demand intercept 120, supply intercept 20, and slopes of 2. Find the per-unit subsidy that produces a government cost of 600 dollars.
- Target: Demand price intercept = 120 dollars/unit; tolerance 0 dollars/unit.
- Target: Supply price intercept = 20 dollars/unit; tolerance 0 dollars/unit.
- Target: Demand slope magnitude = 2 dollars/unit²; tolerance 0 dollars/unit².
- Target: Supply slope = 2 dollars/unit²; tolerance 0 dollars/unit².
- Target: Government cost = 600 dollars; tolerance 0.01 dollars.