Annual demand and supply for the Entronics company is given by:QD = 5,000 + 0.5 I + 0.2 A - 100P, and QS = -5000 + 100Pwhere Q is the quantity per year, P is price, I is income per household, and A is advertisingexpenditure.a. If A = $10,000 and I = $25,000, what is the demand function for this firm?b. Given the demand function in part a., what is equilibrium price and quantity?c. If consumer incomes increase to $30,000, what will be the impact on equilibrium price andquantity?
Question
Annual demand and supply for the Entronics company is given by:QD = 5,000 + 0.5 I + 0.2 A - 100P, and QS = -5000 + 100Pwhere Q is the quantity per year, P is price, I is income per household, and A is advertisingexpenditure.a. If A = 25,000, what is the demand function for this firm?b. Given the demand function in part a., what is equilibrium price and quantity?c. If consumer incomes increase to $30,000, what will be the impact on equilibrium price andquantity?
Solution
a. To find the demand function, we need to substitute the given values of A and I into the demand equation.
The demand equation is QD = 5,000 + 0.5I + 0.2A - 100P.
Substituting A = 25,000, we get:
QD = 5,000 + 0.5(25,000) + 0.2(10,000) - 100P QD = 5,000 + 12,500 + 2,000 - 100P QD = 19,500 - 100P
So, the demand function for this firm is QD = 19,500 - 100P.
b. To find the equilibrium price and quantity, we need to set the demand function equal to the supply function and solve for P.
The supply function is QS = -5000 + 100P.
Setting QD = QS, we get:
19,500 - 100P = -5000 + 100P 24,500 = 200P P = 24,500 / 200 P = $122.5
Substituting P = $122.5 into either the demand or supply function to find the equilibrium quantity Q:
Q = 19,500 - 100(122.5) Q = 19,500 - 12,250 Q = 7,250
So, the equilibrium price is $122.5 and the equilibrium quantity is 7,250.
c. If consumer incomes increase to $30,000, we need to substitute this new value into the demand function and then find the new equilibrium price and quantity.
The new demand function is:
QD = 5,000 + 0.5(30,000) + 0.2(10,000) - 100P QD = 5,000 + 15,000 + 2,000 - 100P QD = 22,000 - 100P
Setting the new QD equal to QS, we get:
22,000 - 100P = -5000 + 100P 27,000 = 200P P = 27,000 / 200 P = $135
Substituting P = $135 into either the new demand or supply function to find the new equilibrium quantity Q:
Q = 22,000 - 100(135) Q = 22,000 - 13,500 Q = 8,500
So, if consumer incomes increase to 135 and the new equilibrium quantity will be 8,500.
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