The market demand and supply functions for imported cars are: QD = 800,000 - 5P

Question

The market demand and supply functions for imported cars are: QD = 800,000 - 5P and QS = 14 P + 225,000. The legislature is considering a tariff (a tax on imported goods) equal to $2,000 per unit to aid domestic car manufacturers. If the tariff is implemented, calculate the loss in producer surplus. How many units of cars are imported? Suppose that instead of a tariff, importers agree to voluntarily restrict their imports to this level. If they do and no tariff is implemented, calculate producer surplus in this scenario. Do you expect importers will be more in favor of a tariff or a voluntary quota?

Explanation / Answer

Step 1: Solving for the equilibrium price and quantity

QD = 800000 – 5P

QS = 14P + 225000

At equilibrium, QD = QS

Therefore,

800000 – 5P = 14P + 225000

19P = 575000

P = 575000 / 19 = 30263.16

To find the equilibrium, put P = 30263.16 in either Demand function or Supply function

QD = 800000 – 5 (30263.16) = 648684.21 = 648684 (Rounding off)

QS = 14(30263.16) + 225000 = 648684.24 = 648684 (Rounding off)

Step 2: Solving for Producer Surplus

Producer surplus is the total amount by which the producers came out ahead. It’s equal to the area between equilibrium and supply.

Both areas can be found using a definite integral. In the graph if we plot demand function and supply function and mark the equilibrium price,

The left edge of Producer Surplus is the point where the supply function crosses the x-axis, and so to find this point, we set the supply function equal to zero and solve:

QS = 14P + 225000 = 0

The right edge is easy: it’s the equilibrium line, and the x-coordinate of that line is 30263.16. So the bounds of our integral will be $- 16071.42 and $30263.16. The upper function this time is our supply equation, and the lower function is zero. This leads to the integral:

                                                     30263.16

This leads to the integral : - 16071.42 (14P + 225000) – 0dp

= 14 P2/2 + 225000P + C 30263.16

- 16071.42

= [14 (30263.16) 2/2 + 225000(30263.16)] - [14 (- 16071.42 ) 2/2 + 225000((- 16071.42 )]

Note: Check the supply function for accuracy before solving

For increase in tariff, supply function will become: 14(P+ 2000) + 225000 and steps should be repeated. The difference between the new producer surplus and old producer surplus may be calculated after that.

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