2.Scenario

In the island nation of Autarka, electricity is primarily generated by burning fossil fuels,

a significantcant contributor to climate change. The government has proposed introducing a

60% tax on retail electricity prices to provide consumers with an incentive to save electricity

and purchase more energy efficient appliances.

Community groups in Autarka have expressed concern that the proposed tax will dis-

proportionately hurt low income households. These households spend a larger proportion

of their income on energy, and may not be able to afford to purchase new appliances.

In response, the government has suggested providing compensation to low income

households to ensure that they are no worse o. However, some commentators have

criticised this suggestion, claiming that compensation would be too expensive, and drive

up demand for electricity amongst low income households.

2.1 Your task

Your task is to estimate the impact of the proposed tax on low-income households, and

determine the level of compensation necessary to ensure that they are no worse o as a

result of the tax. You are also to assess the claims regarding the cost of compensation,

and effect of compensation on low-income household demand for electricity.

2.2 Low-income households

Using data from household surveys, you have determined that the `typical' low-income

household has a monthly income of $2400. The household's preferences are represented

by the utility function,

U = x²y ;

where x represents the quantity of electricity consumed, measure in Megawatt hours

(Mwh), and y represents the quantity of the composite good consumed. The associate

marginal utilities are,

MU_x = 2xy and MU_y = x²:

The price of electricity is currently P_x = $100 per Mwh, and the price of the composite

good is normalised to P_y = 1.

3.2 Analysis

The second section in your reports is the analysis section. In this section you must complete

each of the steps detailed below. The required analysis draws on content covered in lectures

1{5. When completing the steps you must:

Type all equations using the `Insert Equation' function (or equivalent).

Show all of your working and include sufficient written description for the reader to

follow your process.

Note that hand draw figures and equations are not acceptable. There is no word/page

limit for the analysis section.

Step 1: Derive the marginal rate of substitution for the typical low-income household.

Step 2: Find the household's electricity demand function, and composite good demand

function. Use P_x to represent the price of electricity. You should substitute for P_y and I

using the values in the scenario.

Step 3: Find the household's optimal consumption basket under the initial prices (no tax).

What utility does the household derive from this basket?

Step 4: Find the household's optimal consumption basket if a carbon tax is applied to

electricity. What utility does the household derive from this basket?

Step 5: What level of compensation must the government provide to the low-income

household to restore its welfare to the pre-tax level. Hint: The decomposition consumption

basket delivers the initial level of utility at the final prices.