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.

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.

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_xto represent the price of electricity. You should substitute for P_yand 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.

I need help with Step 5! Thank you