Yell-O Yew-Boats, Ltd. produces a popular brand of pointy birds called Blue Meanies. Consider the demand and supply equations for Blue Meanies:
QD, x = 150 - 2Px + 0.001I + 1.5Py
QS,x = 60 + 4Px - 2.5W
Where Qx = monthly per-family consumption of Blue Meanies
Px = price per unit of Blue Meanies
I = median annual per-family income = $25,000
Py = price per unit of Apple Bonkers = $5.00
W = hourly per-worker wage rate = $8.60
a. What type of good is an Apple Bonker?
b. What are the equilibrium price and quantity of Blue Meanies?
c. Suppose that median per-family income increases by $6,000. What are the new equilibrium price and quantity of Blue Meanies?
Yell-O Yew-Boats, Ltd. produces a popular brand of pointy birds called Blue Meanies. Consider the demand and supply equations for Blue Meanies:
QD, x = 150 - 2Px + 0.001I + 1.5Py
QS,x = 60 + 4Px - 2.5W
Where Qx = monthly per-family consumption of Blue Meanies
Px = price per unit of Blue Meanies
I = median annual per-family income = $25,000
Py = price per unit of Apple Bonkers = $5.00
W = hourly per-worker wage rate = $8.60
a. What type of good is an Apple Bonker?
b. What are the equilibrium price and quantity of Blue Meanies?
c. Suppose that median per-family income increases by $6,000. What are the new equilibrium price and quantity of Blue Meanies?
please help me for this question. I need the answer of the question.
Thank you
QD,X=150-2PX+0.001I+1.5PY
answer
a. To determine the type of good an Apple Bonker is, we can refer to the demand equation for Blue Meanies. In the demand equation, the coefficient of Py (price of Apple Bonkers) gives us information about the relationship between the two goods. If the coefficient is positive, it means that Blue Meanies and Apple Bonkers are substitutes. If the coefficient is negative, it means that they are complements.
In this case, the demand equation is: QD, x = 150 - 2Px + 0.001I + 1.5Py
Since the coefficient of Py is positive (1.5), it indicates that Blue Meanies and Apple Bonkers are substitutes. Therefore, an Apple Bonker is a substitute good for Blue Meanies.
b. To find the equilibrium price and quantity of Blue Meanies, we need to set the quantity demanded equal to the quantity supplied and solve for Px.
Setting QD,x (quantity demanded) equal to QS,x (quantity supplied):
150 - 2Px + 0.001I + 1.5Py = 60 + 4Px - 2.5W
Now, substitute the given values:
I = $25,000
Py = $5.00
W = $8.60
The equation becomes:
150 - 2Px + 0.001(25000) + 1.5(5.00) = 60 + 4Px - 2.5(8.60)
Simplify the equation:
150 - 2Px + 25 + 7.5 = 60 + 4Px - 21.5
Combine like terms:
182.5 - 2Px = 4Px - 39.5
Add 2Px to both sides:
182.5 = 6Px - 39.5
Add 39.5 to both sides:
222 = 6Px
Divide both sides by 6:
Px = 37
Now, substitute this equilibrium price (Px = 37) back into either the demand equation or supply equation to find the equilibrium quantity.
Using the supply equation QS,x = 60 + 4Px - 2.5W:
QS,x = 60 + 4(37) - 2.5(8.60)
QS,x = 60 + 148 - 21.5
QS,x = 186.5
Therefore, the equilibrium price of Blue Meanies is $37 and the equilibrium quantity is approximately 186.5.
c. To determine the new equilibrium price and quantity of Blue Meanies when median per-family income increases by $6,000, we need to update the value of I in the demand equation and then solve as before.
The updated value of I is: I = $25,000 + $6,000 = $31,000
Now, substitute this updated value (I = $31,000) into the demand equation to find the new equilibrium price and quantity.
150 - 2Px + 0.001(31000) + 1.5(5.00) = 60 + 4Px - 2.5(8.60)
Simplify and solve as before to find the new equilibrium price and quantity of Blue Meanies.