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.

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