Analyzing the Supply Function for Product X
In this analysis, we will explore the supply function for product X and investigate the quantity of product X produced at different price levels when Px and Pz are given.
Quantity of Product X Produced
1. When Px = $600 and Pz = $60:
[ Q_{xs} = 30 + 2(600) – 4(60) ]
[ Q_{xs} = 30 + 120 – 240 ]
[ Q_{xs} = -90 ]
When Px = $600 and Pz = $60, the quantity of product X produced is -90 units. This negative value suggests a discrepancy in the supply function calculation at these price levels.
2. When Px = $80 and Pz = $60:
[ Q_{xs} = 30 + 2(80) – 4(60) ]
[ Q_{xs} = 30 + 160 – 240 ]
[ Q_{xs} = -50 ]
At Px = $80 and Pz = $60, the quantity of product X produced is -50 units, indicating a potential issue with the supply function’s accuracy.
Determining Supply Function and Inverse Supply Function
Given Pz = $60, the supply function for product X is:
[ Q_{xs} = 30 + 2P_x – 4(60) ]
[ Q_{xs} = 30 + 2P_x – 240 ]
[ Q_{xs} = -210 + 2P_x ]
The inverse supply function can be calculated by solving for Px in terms of Qxs:
[ Q_{xs} = -210 + 2P_x ]
[ Q_{xs} + 210 = 2P_x ]
[ P_x = \dfrac{Q_{xs} + 210}{2} ]
Graphing the Inverse Supply Function
To graph the inverse supply function, we can use the equation derived above:
[ P_x = \dfrac{Q_{xs} + 210}{2} ]
By plotting this equation with Px on the y-axis and Qxs on the x-axis, we can visualize the relationship between price and quantity supplied. The positive slope of the inverse supply curve indicates that as the price of product X increases, the quantity supplied also increases.
Understanding the supply function and its implications for production levels at different price points is essential for businesses to optimize their operations and pricing strategies. By analyzing various scenarios and considering market dynamics, companies can make informed decisions to adapt to changing conditions effectively.
