= ∑ <u>,</u> nn ccm ccggnn ii ∑ ccm ccggnn ii=1 ii ii RR,ii PP ∗QQ ii nn ii PP ii=1 RR,ii where, the average cost of emission for generator QQ, are the unit dispatched by a generator ccm ccggnn ii generator at a 15-minute interval and ∑ are total units generated by all units. The mean cost ii,ii RR,ii PP uu QQ of carbon using these calculations is Rs. 2.08 with a standard deviation of 0.08. nn ii ii=1 RR,ii uu QQ Combining the four components of the marginal cost of electricity consumption: the area clearing price from the wholesale market, the emission costs, and the transmission and distribution losses at 15-minute intervals estimates the SMC for Rajasthan. Electricity duty and urban cess charges are also added to this value. Figure 16 shows the distribution of social marginal cost (SMC) across all periods in the sample. The mean value of marginal cost of electricity inclusive of the social cost of carbon is Rs. 8.2/kWh. Excluding the social cost of carbon reduces the mean marginal price to Rs. 5.5/kWh. The latter price (i.e, Rs. 5.5/kWh) is used for counterfactual tariff calculations, as the high share of thermal generation in Rajasthan’s energy mix<sup>27</sup> makes the carbon-inclusive SMC to be practically infeasible. In the following sections, we analyze the welfare implications of setting the energy price at this price.

# **(i) Distortionary effects of current retail prices**

The deadweight loss of pricing above or below the SMC can be calculated using the range of elasticities from the structural demand model. The deadweight loss represents the difference between the marginal benefit and the marginal cost of consuming an extra unit of electricity. Figure 17 illustrates the procedure for calculating the deadweight losses based on the demand curve, the current energy prices, the SMC and the own-price elasticity. The deadweight loss is the area of the shaded triangle indicated in the figure. Since the SMC is below the current marginal prices (and therefore < ) in this illustration, the deadweight loss for this household is indicative of loss of consumption even though the marginal benefit of consuming an additional unit for the household would have been more QQ<sup>dd</sup> QQ<sup>opt</sup> than its marginal cost. Conversely, for households that have their current energy prices below the SMC (households in the first consumption tier for example), the deadweight loss will indicate excess consumption.

Table 12 summarizes the deadweight losses across income quintiles for FY16-17. The columns show the results over the range of own-price elasticities. A more elastic demand response implies greater sensitivity of consumption to price distortions from SMC. As a result, the deadweight loss estimates are greater for more elastic demand. Estimates of average deadweight loss for households in the first quintile are in the range of Rs. 3.1 to Rs. 12.4 per month and highest across all other categories.

> 27 Existing literature suggests that there are significant differences between domestic and global values of the social cost of carbon (SCC) exists, but these papers provide limited agreement on the distribution of the global SCC by countries. Moreover, the existing literature appears to suggest a range of carbon costs: from Nordhaus (2018) estimate of $33.60 / tCo2 to EPA’s estimate of $12, $42 and $62 per tCO2 at 5, 3 and 2.5% discount rates. Reconciling the calculations undertaken in the past literature (using a combination of IAM models and growth assumptions) to calculate a robust SCC estimate for India is outside the scope of this paper. However, in a recent paper Ricke, Drought, Caldeira and Tavoni (2018), estimate that India’s share of global SCC is 21%. Our best approximation would be to use Nordhaus’ estimate of $33.60 / tCo2 to calculate India’s share of global SCC = .21*33.60 = Rs. 458.64/ tCo2. Backof-the envelope calculations suggest that this will increase the SMC to approximately Rs. 6.13/kWh (a 11.4% increase from the current estimate of Rs. 5.5/kWh). We do not consider this as a separate counterfactual exercise but show the welfare impact of including the domestic cost of SCC into SMC in footnote 31.

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