Annual demand and supply for the Entronics company is given by:
QD = 5,000 + 0.5 I + 0.2 A - 100P, and QS = -5000 + 100P
where Q is the quantity per year, P is price, I is income per household, and A is advertising expenditure.
a. If A = $10,000 and I = $25,000, what is the demand curve?
b. Given the demand curve 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 and quantity?
To solve this problem, we will substitute the given values into the demand equation and solve for the variables.
a. If A = $10,000 and I = $25,000, we can substitute these values into the demand equation to find the demand curve:
QD = 5,000 + 0.5 I + 0.2 A - 100P
By substituting the values, we get:
QD = 5,000 + 0.5 * 25,000 + 0.2 * 10,000 - 100P
Simplifying this equation gives:
QD = 5,000 + 12,500 + 2,000 - 100P
QD = 19,500 - 100P
Therefore, the demand curve with A = $10,000 and I = $25,000 is QD = 19,500 - 100P.
b. To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied. The quantity supplied is given by QS = -5000 + 100P.
Setting QD equal to QS, we have:
19,500 - 100P = -5000 + 100P
Adding 100P to both sides and adding 5000 to both sides, we get:
24,500 = 200P
Dividing both sides by 200, we find:
P = 122.5
Substituting this value of P back into either QD or QS, we find:
Q = 19,500 - 100 * 122.5 = 7,250
Therefore, the equilibrium price is $122.5 and the equilibrium quantity is 7,250.
c. If consumer incomes increase to $30,000, we need to find the new demand curve and then determine the impact on the equilibrium price and quantity.
We can substitute the new value of I into the demand equation and solve for the new demand curve:
QD = 5,000 + 0.5 * 30,000 + 0.2 * 10,000 - 100P
QD = 5,000 + 15,000 + 2,000 - 100P
QD = 22,000 - 100P
To find the impact on equilibrium price and quantity, we need to compare the new demand and supply curves. Since the supply curve remains the same (QS = -5000 + 100P), we can set the new demand curve equal to the supply curve:
22,000 - 100P = -5000 + 100P
Adding 100P to both sides and adding 5000 to both sides, we get:
27,000 = 200P
Dividing both sides by 200, we find:
P = 135
Substituting this value of P back into either QD or QS, we find:
Q = 22,000 - 100 * 135 = 8,500
Therefore, with consumer incomes increasing to $30,000, the new equilibrium price is $135 and the new equilibrium quantity is 8,500.