Part 1: Spatial Equilibrium In Market 1 Demand Is D1 At P1
Part 1 Spatial Equilibriumthe Demand In Market 1 Is D1 24 P1the S
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. If no trade occurs between the markets, what are the equilibrium values of D1, S1, P1, D2, S2, and P2? Solve algebraically.
2. If the cost of transportation between the two markets is PT = 2, what would be the equilibrium values of D1, S1, P1, D2, S2, P2, QT, and PT? 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: QD1 = 24 – P1. In the second period, it is: QD2 = 18 - P2.
1. 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]
2. 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]
3. By comparing the results for 5 and 6 above, explain how the cost of storage affects prices and quantities in each period.
Paper For Above instruction
The comprehensive analysis of spatial and storage equilibrium offers critical insights into market behaviors, price formation, and strategic decision-making for producers and policymakers. Integrating equilibrium analysis with graphical representations deepens understanding and illustrates the practical implications of economic principles. This paper addresses algebraic solutions for market equilibrium without and with transportation costs, and explores the effects of storage cost on market dynamics across two periods for potatoes, providing visual illustrations and interpretations.
Spatial Equilibrium without Trade
First, considering the scenario where no trade occurs between two markets, the equilibrium in each market can be found by setting demand equal to supply. For Market 1, demand D1 = 24 - P1, and supply S1 = -2 + P1. Equilibrium occurs where D1 = S1:
24 - P1 = -2 + P1
Adding P1 to both sides and adding 2 to both sides:
24 + 2 = P1 + P1
26 = 2P1
P1 = 13
Substituting P1 into demand or supply to find D1 and S1:
D1 = 24 - 13 = 11; S1 = -2 + 13 = 11
Similarly, for Market 2, demand D2 = 16 - P2, and supply S2 = 2 + P2. Setting D2 = S2:
16 - P2 = 2 + P2
16 - 2 = P2 + P2
14 = 2P2
P2 = 7
Demand D2 = 16 - 7 = 9; Supply S2 = 2 + 7 = 9
Therefore, the equilibrium values without trade are:
- P1 = 13, D1 = 11, S1 = 11
- P2 = 7, D2 = 9, S2 = 9
Equilibrium with Transportation Costs
Introducing a transportation cost PT = 2 modifies the effective price in the second market, raising the cost for goods transported from Market 1 to Market 2. The effective price for Market 2 becomes P2 + PT. To find equilibrium, the conditions should satisfy that the price difference compensates for transportation costs, aligning supply and demand accordingly.
The new relationship, considering transportation costs, is:
D2 = 16 - P2
and the price including transport is P2 + PT. Similarly, a price in Market 1 influences the second market:
P1 = P2 + PT
with the equilibrium condition adjusting to:
D1 = S1 at P1 = P2 + 2
and D2 = S2 at P2 considering P2 + 2. Solving these systematically yields:
From previous D1 and S1, P1 remains 13 and D1 = 11. Since P1 = P2 + 2, then P2 = P1 - 2 = 13 - 2 = 11.
Calculating D2 and S2 at P2 = 11:
D2 = 16 - 11 = 5; S2 = 2 + 11 = 13.
Since D2 ≠ S2, equilibrium occurs when demand equals supply, but considering transportation costs, the prices adjust so that the quantities align. The feasible equilibrium point is P2 = 11, with quantities D2 = 5 and S2 = 13, and P1 = 13, with D1 = S1 = 11.
Graphical Representations
Graphing the market without trade involves plotting the individual demand and supply curves for both markets intersecting at their equilibrium points, with price on the vertical axis and quantity on the horizontal axis.
With trade and transportation costs, the graphs shift to illustrate the divergence in prices between the markets, and the cost wedge created by transportation costs is visually represented by the difference in prices at the same quantities, showing how trade can lead to price equalization adjusted for transport expenses.
Storage Equilibrium for Potatoes
The storage scenario introduces intertemporal considerations. The supply curve Qs1 = 12 + 0.5P intersects with demand curves in two periods: QD1 = 24 - P1 (first period) and QD2 = 18 - P2 (second period). When storage costs are zero, prices and quantities adjust solely based on demand and supply interaction, with elasticities dictating the shift.
In the no-storage-cost case, equilibrium occurs where supply equals demand in each period independently. For period 1, setting Qs1 = QD1:
12 + 0.5P1 = 24 - P1
Adding P1 to both sides:
12 + 0.5P1 + P1 = 24
12 + 1.5P1 = 24
1.5P1 = 12
P1 = 8
Quantity in period 1:
Qx = 12 + 0.5*8 = 12 + 4 = 16
In period 2, setting Qs1 equal to QD2:
12 + 0.5P2 = 18 - P2
12 + 0.5P2 + P2 = 18
12 + 1.5P2 = 18
1.5P2 = 6
P2 = 4
Quantity in period 2:
Qx = 12 + 0.5*4 = 12 + 2 = 14
When storage costs are introduced ($5 per cwt), the incentives to store or defer sales change. Storage costs reduce the profitability of carrying potatoes into the second period, generally decreasing second-period prices and increasing first-period prices, as storage becomes less attractive. Graphically, the shift in the demand curves reflects higher prices in the first period and lower prices in the second, with the quantities adjusting accordingly.
Approximating, with storage costs, the second-period price P2 may decrease to reflect the cost of storage, adjusting the demand curve downward. The first period's price P1 will increase, as sellers prefer to sell earlier rather than store and incur the cost. Quantities adjust in proportion to these shifts, generally leading to decreased second-period quantities and increased first-period quantities.
Impacts of Storage Costs on Prices and Quantities
The comparison demonstrates that increases in storage costs discourage holding inventory for later sale, resulting in lower second-period prices, reduced second-period quantities, and elevated first-period prices. Conversely, when storage costs are zero, the market equilibrates optimally across periods, facilitating price arbitrage and inventory balancing. Therefore, storage costs act as a critical regulatory factor affecting intertemporal pricing and market behavior.
Conclusion
The algebraic and graphical analyses of spatial equilibrium and storage dynamics highlight the importance of transportation costs and storage costs in shaping market outcomes. Understanding these factors helps policymakers and market participants optimize trading strategies, inventory management, and pricing policies. Accurate modeling and visualization inform better decision-making in complex economic systems, demonstrating the interconnectedness of spatial and temporal market forces.
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