Reference no: EM132618043

Using data from household surveys, you have determined that the 'typical' low-income household has a monthly income of $1800. The household's preferences are represented by the utility function, 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,

MUx = y2 and MUy = 2xy.

The price of electricity is currently Px = $100 per Mwh, and the price of the composite good is normalised to Py = 1.

The government has proposed introducing a 50% tax on retail electricity prices to provide consumers with an incentive to save electricity and purchase more energy efficient appliances.

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 Px to represent the price of electricity. You should substitute for Py 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.