radnorgardens
New member
- Joined
- Dec 2, 2014
- Messages
- 26
Hi all,
Trying to solve the following problem from Mathematics for Economics and Business by Ian Jacques - Supply and Demand Analysis. The demand and supply functions of a good are given by
P = -5Q + 80
P = 2Q + 10
For this first part I've already worked out the equilibrium price and quantity. P = 30; Q = 10
Next, if there's 15% government tax on the market price, determine the new equilibrium price and quantity. I had no issue when the question provide a nominal amount i.e. £5, but I'm struggling with the %age. I'm know this only affects the supply equation.
So I thought it would start as follows:
P x 1.15 = 2Q + 10 (divide both sides by 1.15)
P = (2Q + 10) / 1.15
Then
-5Q + 80 = (2Q + 10) / 1.15 (multiple both sides by 1.15)
-5Q + 80 x 1.15 = 2Q + 10 (add 5Q both sides)
80 x 1.15 = 7Q + 10 (minus 10 both sides)
70 x 1.15 = 7Q
80.5 = 7Q (divide both sides by 7)
11.5 = Q
But the answer key starts the answer as
0.85P = 2Q + 10
P = 33.6
Q = 9.28
I thought the tax was added on, hence 1.15, but it's seems it's deducted, so 0.85 - why is that?
Anyway, I used 0.85 and still got the wrong answer.
0.85 x P = 2Q + 10 (divide both sides by 0.85)
P = (2Q + 10) / 0.85
Then
-5Q + 80 = (2Q + 10) / 0.85 (multiple both sides by 0.85)
-5Q + 80 x 0.85 = 2Q + 10 (add 5Q both sides)
80 x 0.85 = 7Q + 10 (minus 10 both sides)
70 x 0.85= 7Q
59.5 = 7Q (divide both sides by 7)
8.5 = Q
Where am I going wrong?
Thank you for any help.
Trying to solve the following problem from Mathematics for Economics and Business by Ian Jacques - Supply and Demand Analysis. The demand and supply functions of a good are given by
P = -5Q + 80
P = 2Q + 10
For this first part I've already worked out the equilibrium price and quantity. P = 30; Q = 10
Next, if there's 15% government tax on the market price, determine the new equilibrium price and quantity. I had no issue when the question provide a nominal amount i.e. £5, but I'm struggling with the %age. I'm know this only affects the supply equation.
So I thought it would start as follows:
P x 1.15 = 2Q + 10 (divide both sides by 1.15)
P = (2Q + 10) / 1.15
Then
-5Q + 80 = (2Q + 10) / 1.15 (multiple both sides by 1.15)
-5Q + 80 x 1.15 = 2Q + 10 (add 5Q both sides)
80 x 1.15 = 7Q + 10 (minus 10 both sides)
70 x 1.15 = 7Q
80.5 = 7Q (divide both sides by 7)
11.5 = Q
But the answer key starts the answer as
0.85P = 2Q + 10
P = 33.6
Q = 9.28
I thought the tax was added on, hence 1.15, but it's seems it's deducted, so 0.85 - why is that?
Anyway, I used 0.85 and still got the wrong answer.
0.85 x P = 2Q + 10 (divide both sides by 0.85)
P = (2Q + 10) / 0.85
Then
-5Q + 80 = (2Q + 10) / 0.85 (multiple both sides by 0.85)
-5Q + 80 x 0.85 = 2Q + 10 (add 5Q both sides)
80 x 0.85 = 7Q + 10 (minus 10 both sides)
70 x 0.85= 7Q
59.5 = 7Q (divide both sides by 7)
8.5 = Q
Where am I going wrong?
Thank you for any help.