The supply curve is given by Qs =-200 + 20px-5P + 0.5Pr where Qs quantity supplied of good X Px price of good X Pr- price of inputs to good X a. Based on the supply curve above, what is the b. What is the equation of the supply curve if input
The Correct Answer and Explanation is :
Let’s break down the supply curve provided and answer your questions step by step.
The supply curve is given by the equation:
[
Q_s = -200 + 20P_x – 5P + 0.5P_r
]
Where:
- (Q_s) = Quantity supplied of good X,
- (P_x) = Price of good X,
- (P) = Price of another related good,
- (P_r) = Price of inputs to good X.
a. Based on the supply curve above:
The supply curve shows the relationship between the quantity of a good that producers are willing to supply (quantity supplied, (Q_s)) and various factors that influence this decision, including the price of the good itself ((P_x)), the price of another related good ((P)), and the price of inputs ((P_r)).
In this case, the term (20P_x) indicates that as the price of good X increases ((P_x)), the quantity supplied of good X increases. This aligns with the basic law of supply, which states that as the price of a good rises, suppliers are willing to produce and offer more of it for sale.
The term (-5P) represents how the price of a related good (let’s assume it’s a substitute or complementary good) influences the quantity supplied. The negative sign means that if the price of this related good increases, the quantity supplied of good X decreases.
Lastly, (0.5P_r) shows how the price of inputs ((P_r)) affects the supply of good X. An increase in the price of inputs will raise production costs, which in turn reduces the quantity supplied, as producers may not find it profitable to produce as much.
b. The equation of the supply curve if the price of inputs increases:
If the price of inputs ((P_r)) increases, the term (0.5P_r) will increase. This leads to an increase in the quantity supplied of good X, as the effect of higher input prices shifts the supply curve. The new equation will reflect the changes in (P_r).
To provide a graphical representation, I’ll generate a plot showing how the supply curve might shift based on changes in input prices.
Let me create that for you!
Here is the graph showing the effect of an increase in the price of inputs ((P_r)) on the supply curve. The original supply curve is represented by the blue line, and the red dashed line represents the supply curve when the price of inputs increases.
As you can see, when the price of inputs rises, the supply curve shifts upward (or to the left), which indicates a decrease in the quantity supplied at each price level. This is because higher input prices make it more expensive for producers to produce the good, so they are less willing to supply the same quantity.
This shift reflects the inverse relationship between input prices and supply: as input costs rise, the quantity supplied decreases, leading to a shift in the supply curve.
