Question

Part I. In Cauland, people’s consumption X depends on their income levels as the following consumption function shows. X = a + bY , where a > 0 and 0<b<1. Suppose the government imposes a 10% flat tax on consumption.

1. How does the amount of a person’s consumption tax change as the person’s income increases?

2. How does the average tax rate change as the person’s income increases?

3. How does the marginal tax rate change as the person’s income increases?

4. Is this tax regressive, progressive, or proportional?

Part II. The marginal cost of producing Hwatoo (or Hanafuda) sets is constant at ₩ 1,000 per a set in the competitive market. Though the market demand is known to be perfectly inelastic, the compensated (Hicksian) demand for the Hwatoo sets in Dobakia is given as follows. Q = 500 – 0.1 P if P < 5000, and Q = 0 otherwise. Now suppose the government levies a 100-won unit tax on the consumption of a Hwatoo set, as they want to discourage people from playing with Hwatoo.

1. How much is the gross price of a Hwatoo set after the tax?

2. How much is the tax revenue collected by the government?

3. How much is the excess burden?

4. Draw a diagram of the indifference curves and budget constraints. Can you still find the excess burden in this diagram?

5. Define the average excess burden as the ratio of total excess burden to total revenue. How much is the average excess burden? Round numbers up at the 6th decimal place if necessary.

6. Now the government wants to raise ₩1 of revenue more than what they raise under the current 100-won unit tax. Therefore, the government should raise the tax rate. Suppose the new tax rate is t*. Then, P* = 1000 + t* = 5000 – 10Q*. That is, Q* = 400 – 0.1t*. The revenue after raising the tax rate is Q*t* = (400 – 0.1t*)t* = 39000 +1 = 39001. 0.1(t*)2 – 400t* + 39001 = 0. And t* = 100.002632. Then, how much is the marginal excess burden in this case? Use a computer or calculator. Round numbers up at the 6th decimal place if necessary.

7. Which is greater between the average excess burden and the marginal excess burden?

8. In the given situation, would the average excess burden increase or decrease if we raise more tax revenue?

Answer 1

Answering only part 1 with first 4 parts

1) as flat tax rate of 10% is applied.

So consumption tax rise linearly with rise in income

As Consumpltion tax , C_{​​​​​​t} = .1(a+bY)

2) average tax rate remains unchanged as income rise & equals

10%

3) marginal as rate is same as average tax rate .

4) this is a proportional tax rate system , since Everyone pays the same tax irrespective of income level .

Thus same tax rate is applied on every one , regardless of income level