What is the maximum amount you would pay for an asset that generates an income of $250,000 at the end of each of five years if the opportunity cost of using funds is 8%?
Sample Answer
Sample Answer
Analyzing the Supply Function for Product X
In this analysis, we will delve into the supply function for product X and explore how changes in price affect the quantity supplied. The supply function is given by:
[ Q_{xs} = 30 + 2P_x – 4P_z ]
Quantity of Product X Produced
1. When Px = $600 and Pz = $60:
[ Q_{x1s} = 30 + 2(600) – 4(60) ]
[ Q_{x1s} = 30 + 120 – 240 ]
[ Q_{x1s} = 150 ]
Therefore, when Px = $600 and Pz = $60, 150 units of product X are produced.
2. When Px = $80 and Pz = $60:
[ Q_{x2s} = 30 + 2(80) – 4(60) ]
[ Q_{x2s} = 30 + 160 – 240 ]
[ Q_{x2s} = -50 ]
In this case, when Px = $80 and Pz = $60, the quantity supplied is -50 units. This negative value indicates that at this price combination, there may be a surplus or that the supply function may not be accurately reflecting the market dynamics.
Supply Function and Inverse Supply Function
Given that Pz = $60, we can determine the supply function for product X by substituting Pz into the original supply function:
[ Q_{xs} = 30 + 2P_x – 4(60) ]
[ Q_{xs} = 30 + 2P_x – 240 ]
[ Q_{xs} = -210 + 2P_x ]
The inverse supply function can be derived 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 on a graph with Px on the y-axis and Qxs on the x-axis, we can visualize how changes in quantity supplied affect the price of product X. The slope of the inverse supply curve will be positive, indicating a direct relationship between price and quantity supplied.
Understanding the supply function and its implications on quantity supplied at different price levels is crucial for analyzing market dynamics and making informed decisions regarding production levels and pricing strategies for product X. By considering various price scenarios and the corresponding quantity supplied, businesses can optimize their production processes and adapt to changing market conditions effectively.
