Question

Consider a market in which aggregate demand is given by 1000−10p, and aggregate supply is given by 10p, where p denotes the market price.

QUESTION: What is the maximum amount of revenue that the government can raise using a per-unit sales tax on consumers?

Answer 1

25000

Answer 2

wrong !!!

Answer 3

So what's correct?

Answer 4

This is the total social welfare available.

Answer 5

Ok, The correct answer should be 12,500. Let me know if you are happy with this.

Answer 6

correct!!!! thnks dude

Answer 7

Thanks

Answer 8

Thanks!

Answer 9

[AI-generated answer — Explain Bot]

To determine the maximum amount of revenue the government can raise using a per-unit sales tax on consumers, we need to find the price at which the quantity demanded equals the quantity supplied. This price is called the equilibrium price and is denoted by "p*".

First, we need to set the quantity demanded equal to the quantity supplied:

1000 - 10p = 10p

Now, let's solve for "p":

1000 = 20p

Dividing both sides of the equation by 20, we get:

p = 50

So, the equilibrium price is 50.

To calculate the maximum amount of revenue, we need to find the quantity sold at this equilibrium price. We can substitute the equilibrium price (p*) into either the demand or supply equation to find the corresponding quantity. Let's use the demand equation:

Q = 1000 - 10p*
Q = 1000 - 10(50)
Q = 1000 - 500
Q = 500

Thus, at the equilibrium price of 50, the quantity demanded and supplied is 500.

Now, to calculate the maximum revenue with the sales tax, you need to determine the new price faced by consumers after the per-unit tax is implemented. Let's denote this new price as "p_t" (subscript 't' for tax).

If the tax per unit is denoted as "t", then the new price faced by consumers (p_t) can be expressed as:

p_t = p + t

The government revenue per unit will be equal to the tax per unit. So the revenue raised by the government (R) is given by:

R = t * Q

To maximize revenue, we need to choose the value of "t" such that it maximizes "R". Since the government revenue is equal to the tax per unit multiplied by the quantity sold, the maximum government revenue will occur when the tax per unit is applied to the entire quantity sold, which in this case is 500.

Therefore, the maximum amount of revenue that the government can raise using a per-unit sales tax on consumers is:

R = t * Q
R = t * 500

Please note that we don't have specific values for the tax per unit ("t"), so we can't provide an exact numerical answer. Nonetheless, using the formula provided, you can substitute a value for "t" to find the corresponding maximum revenue.