Question

Part 1: Spatial Equilibrium

The demand in market 1 is D₁ = 24 - P₁
The supply in market 1 is S₁ = -2 + P₁
The demand in market 2 is D₂ = 16 - P₂
The supply in market 2 is S₂ = 2 + P₂

1.         If no trade occurs between the markets, what are the equilibrium values of D₁, S_1, P_1, D₂, S₂, and P₂? Solve algebraically.

2.         If the cost of transportation between the two markets is P_T = 2, what would be the equilibrium values of D₁, S₁, P_1, D₂, S₂, P₂, Q_T, and P_T? Solve algebraically.

3.         Show the above situation graphically, both with and without trade. Please label everything.

[Insert an image of your graph here]

Part 2: Storage Equilibrium

Assume that the market supply curve for potatoes is Qs₁ = 12 + 0.5P, and that there are two marketing periods for the crop. In the first marketing period the demand curve is: Q_D1 = 24 – P₁, in the second period it is: Q_D2= 18 - P₂.

Draw a graph of the markets in the two periods showing prices and quantities if it costs nothing to store potatoes. Be sure to label all the relevant features on your graph.

[Insert an image of your graph here]

Show the prices and quantities in each period if it costs $5 per cwt. to store potatoes for delivery in the second marketing period. Again, be sure to label all relevant features on your graph (s).

[Insert an image of your graph here]

By comparing the results for 5 and 6 above explain how the cost of storage affects prices and quantities in each period.

Answer 1

1).

Consider the given problem here the demand and the supply curve of “market1” is given in the question, => in the equilibrium the demand must be equal to the supply.

=> D1 = S1, => 24 – P1 = (-2) + P1, => 2P1 = 26, => P1=13. So, the equilibrium quantity demanded and supplied is given by, “D1 = 24-P1 = 24-13 = 11, => D1=S1=11.

Now, the equilibrium condition of the “market2” is given by, “D2=S2”.

=> 16 – P2 = 2 + P2, => 2*P2 = 14, => P2 = 7. Now, the equilibrium quantity demanded and supplied is given by, “D1 = 16-P2 = 16-7 = 9, => D2=S2=9.

2).

So, here we can see that “P1=13” > “P2=7”, =>”market 1” will import the good form “market 2”. So, the import demand function is given below.

=> IM = D1 – S1 = (24-P1) – (-2 + P1) = 24 – P1 + 2 – P1 = 26 – 2*P1, => IM = 26 – 2*P1.

=> P = 13 – 0.5*IM.

Now, the export supply function is given below.

=> EX = S2 – D2 = (2 + P2) – (16 – P2) = 2 + P2 – 16 + P2 = 2*P2 – 14, => P = 7 + 0.5*EX.

=> P = 7 + 0.5*EX, now because of the transportation cost it is given by.

=> P = 7+2 + 0.5*EX, => P = 9 + 0.5*EX.

So, in the equilibrium these two expression must be same.

=> 13 – 0.5*IM = 9 + 0.5*EX, => 13 – 0.5*Q = 9 + 0.5*Q, => 4 = Q, => Q = IM = EX = 4”.

=> P = 9+0.5*EX = 11, => P=11.

So, the equilibrium “P” is “P1=P2=11, D1 = 24-P1 = 24 – 11 = 13 and S1 = (-2) + P1 = 9.

=> So, in this new price “D1=13” and S1=9”, => import is “D1-S1=4”.

Now, at “P=11”, D2 = 16-P2 = 16 – 11 = 5 and S2 = D2+4 = 9.

=> So, in this new price “D2=5” and S2=9”, => export is “4”.

3).

Consider the following fig shows the equilibrium “P” and “Q” in both matket.

So, here “D1” be the demand curve and “S1” be the supply curve of the “market1”, => under without trade the equilibrium “P” and “Q” will be determined by the condition “S=D1”, => the equilibrium “P1=13” and “S1=D1=11”. Now, “D2” be the demand curve and “S2” be the supply curve of the “market 2”, => under without trade the equilibrium “P” and “Q” will be determined by the condition “S2=D2”, => the equilibrium “P2=7” and “S2=D2=9”

Consider the following fig shows the equilibrium under trade.

So, here the equilibrium export and import will be determined by the condition “IM=EX”, => the equilibrium “P=11” and “IM=EX=4”.