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Policy Inquiry...

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Price Theory ECON1056

POLICY INQUIRY

Introduction This research report represents the findings of the analysis into how the proposed tax of 60% on retail electricity prices in the island nation of Autarka. The government is aiming to reduce the use of electricity in households and to promote the use of more energy efficient appliances. The findings show that the low-income households are going to be directly affected by this as they have minimal income to spend on electricity and composite goods. The substitution effect (0.93) reflects that when price goes up the consumption of electricity goes down.

Analysis Step 1: Marginal Rate of Substitution At the optimum the slope of the indifference curve is equal to the slope of the budget line, therefore, MRS x , y = ¿

MU x MU y

2 xy x2

∴ MRS x , y =

2y x

Step 2: Household’s Electricity & Composite Goods Demand Function Household demand function: Budget Line Equation, Px x+ P y y=I

⇒P x x + y=I Given that

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P y =1 , the tangency condition can be stated as,

MU x Px 2 y = ⇒ =P x x MU y P y x=

2y Px Since

Px =100 ⇒x=

2y 100

Substitute x into the budget constraint function to derive the Household Electricity demand function, given that I=2400, Px

( 2100y )+ y =2,400

⇒

Px ∙2 y + y=2400 100

240,000 ⇒y = 2 Px +100 Therefore, the Household’s electricity demand function is as stated, y=

120,000 + 2,400 Px

Likewise, for the composite goods demand function: Budget Line Equation, Px x+P y y=I ⇒P x x + y=I

Given that MU x MU y

y=

=

Px Py

⇒

Px =100 , the tangency condition can be stated as, 2 y 100 = Py x

200 x Py Since

P y =1 ⇒x=

y 200

Substitute x into the budget constraint function to derive the Household Electricity demand function, given that I=2400, 2 Policy Inquiry

Px

( 200y )+ y =2,400

⇒

Px ∙ y + y=2400 200

⇒y =

480,000 Px +200

Therefore, the Composite Goods Demand Function is as stated, y=

480,000 +2,400 Px

Step 3: Household Optimal Consumption Basket The equation for the budget line can be found by substituting prices and income into, Px x+ P y y=I ⇒100 x+ y=2400 The marginal rate of substitution can be found by substituting for the marginal utilities, MRS x , y =

MU x 2 y = MU y x

The tangency condition equates the marginal rate of substitution with the ratio of prices, MU x 2 y y 100 =100 = ∨ = 1 x MU y x Rearranging the tangency condition to solve for y, y =100 ⇒y=100 x x Substitute for y into the budget line equation, 100 x+ 100 x=2400 ⇒200 x=2400 ∴ x=12

Substitute x=12 in the tangency condition,

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y =100 12 ∴ y =1200 Therefore, the optimal consumption basket contains 12 Mwh of electricity consumed and 1200 composite goods consumed. The utility the average low-income household derives from the basket with initial prices is, U ( 12,1200 )=x 2 y =122 ∙ 1200=172,800 Step 4: Household Optimal Consumption Basket (with carbon tax) The equation for the budget line can be found by substituting prices and income into, Px x+ P y y=I ⇒160 x+ y=2400 The marginal rate of substitution can be found by substituting for the marginal utilities, MRS x , y =

MU x MU y

=

2y x

The tangency condition equates the marginal rate of substitution with the ratio of prices, MU x 2 y y 160 =160 = ∨ = 1 x MU y x Rearranging the tangency condition to solve for y, y =160 ⇒y=160 x x Substitute for y into the budget line equation, 160 x+ 160 x=2400 ⇒320 x=2400 ∴ x=7.5

Substitute x=7.5 in the tangency condition, y =160 7.5 4 Policy Inquiry

∴ y =1200 Therefore, the optimal consumption basket contains 7.5 Mwh of electricity consumed and 1200 composite goods consumed. The utility the average low-income household derives from the basket with prices after carbon tax applied is, U ( 7.5,1200) =x 2 y =7.52 ∙ 1200=67,500 Step 5: Government Compensation Decomposition consumption basket for the price change: Equation for the indifference curve that contains initial pricing basket, where U(12,1200)= 172,800: 2

x y=172,800

Marginal rate of substitution is, MU x 2 y = MU y x

The tangency condition at final price can therefore be written as, MU x P x 2 2 y = ⇒ =160 x MU y P y

Solving the tangency condition and the indifference curve equation simultaneously. Rearranging the tangency condition to solve for y, 2y =160 ⇒y =80 x x Substituting for y into the indifference curve equation, x 2(80 x )=172,800 3

⇒x =

172,800 80

√

∴ x=

3

172,800 =12.93 80

Substituting for x into the tangency condition yields,

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y=80

=1034.13 (√172,800 80 ) 3

The substitution effect, reflecting the change in consumption of electricity between the initial basket and decomposition basket, SE=x D −x A =12.93−12= 0.93

This shows that the utility is higher than of the initial pricing, the quantity of electricity consumed increases by 0.93, showing that this incentive from the government is increasing the demand for electricity.

Conclusion The increase in carbon taxes clearly has a negative affects the low-income household, where when the prices go up from the initial $100 per Mwh to $160 per Mwh (post tax) the utility goes from 172,800 down to 67,500. With the proposed compensation to keep the same utility at the higher price there is still a substitution effect of 0.93 reflecting that the quantity of electricity consumed is higher, thus, increasing demand for electricity in the lower-income household.

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Proposed Carbon Tax Leaving the Less Wealthy, Poorer Research and Analysis show that the low-income households in Austark are worse off even with the proposed compensation. The Austark government has proposed a carbon of 60% on retail electricity prices to promote the use of energy efficient appliances and by doing so lowering the use of electricity. The island nation of Austark generates almost all of its electricity by burning fossil fuels, so by initiating this incentive their main goal is to reduce their carbon footprint and lower the emissions contributing to climate change.

An economic consulting firm, RMIT Price Theory Cohort, has conducted and publicised research on the aforementioned tax regarding electricity pricing. The thorough analysis depicts that the population in the lowerincome threshold are worse off even with the considered compensation. The results highlighted that post tax the consumption of electricity in Megawatt hours is less than half the initial consumption.

It was found that in order to restore welfare in the low-income households a compensation was presented to compensate for the increase in price and decrease in usage. However, the cost to compensate these losses would be too expensive for the government and would further drive up

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demand for electricity, defeating the original intention of reducing emissions.

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