Question

Widgets are produced and consumed both inside and outside Freedonia. Suppose both the domestic (Freedonian) and foreign markets are competitive. Let P denote the per-unit price in Freedonia and Pₒ denotes the per-unit price outside Freedonia. Both prices are measured in Freedonian Dollars for convenience. Demand in Freedonia is

D (P ) = { 0 if P ≥50
100−2P if P <50
​ and demand outside Freedonia is Dₒ(Pₒ) = {0 if Pₒ ≥50
150−3Pₒ if Pₒ <50.
The supply from producers in Freedonia is S (P ) = { 0 if P ≤30
2P − 60 if P >30
and supply from producers outside Freedonia is Sₒ (p) = { 0 if Pₒ ≤10
3Pₒ −30 if Pₒ >10
For each part of this exercise, illustrate your work graphically in addition to your computations.
1. Suppose it is impossible to import widgets into or export widgets out of Freedonia (i.e. there exist two separate markets: "Freedonia" and the "rest of the world"). What are the equilibrium price and quantity in Freedonia? What are the equilibrium price and quantity in the rest of the world? What are the corresponding consumers' surplus and producers' surplus in Freedonia and in the rest of the world?​
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Answer 1

The equilibrium price and quantity in Freedoina are 40 Freedonian Dollars and 20 units, respectively.

In the rest of the world, the equilibrium price and quantity are 45 Freedonian Dollars and 15 units.

Consumer surplus and producer surplus can be calculated as areas of triangles under the demand and supply curves, respectively.

Step-by-step explanation:

To determine the equilibrium price and quantity in Freedonia, we set the domestic demand equal to the domestic supply, which gives us 100 - 2P = 2P - 60.

Solving this equation, we find that the equilibrium price (P) is 40 Freedonian Dollars and the equilibrium quantity is 20 units. In the rest of the world, setting foreign demand equal to foreign supply gives us 150 - 3P_o = 3P_o - 30.

Solving for P_o yields 45 Freedonian Dollars as the equilibrium price and the equilibrium quantity as 15 units.

The consumer surplus in Freedonia is the area above the price and below the demand curve, which forms a triangle with a base of 20 units and a height of 10 Freedonian dollars (50 - 40), hence the consumer surplus is 0.5 * 20 * 10 = 100 Freedonian Dollars.

Similarly, the producer surplus in Freedonia is the area below the price and above the supply curve, forming a triangle with a base of 20 units and a height of 10 Freedonian Dollars (40 - 30), leading to a producer surplus also of 100 Freedonian Dollars.

In the rest of the world, the consumer surplus is calculated as 0.5 * 15 * 5 = 37.5 Freedonian Dollars,

and the producer surplus as 0.5 * 15 * 35 = 262.5 Freedonian Dollars, since the area forms a triangle with height 50 - 45 for consumer surplus and height 45 - 10 for producer surplus.