The graph is sourced by The Economist as Enerdata/McKinsey - but it is not properly referenced or linked, and no data is provided. So far for journalistic transparency. (I'll attempt differently.)

Numbers on household electricity in Germany were the quickest to find. A first stop at Wikipedia, here, presents some data on household electricity in the European perspective, using Eurostat data of the year 2011 for 17 European countries:

While this indicates that Germany's household electricity had become the highest in 2011, in part due to the addition of the renewables surcharge (the EEG-Umlage), this doesn't show the price evolution through the years. Additionally, Germany's household bills are hardly "40-50% above the EU average" in 2011.

Wikipedia also presents data, from BDEW, the German association of energy and water companies. It is useful to observe how, by 2013, the German electricity price is constituted by at least seven additional components, after the costs for production, transportation and distribution. This includes one license fee funding local authorities (Konzessionsabgabe) and one federal tax (Stromsteuer). Additionally, there is the VAT (Umsatzsteuer), which appears to be raised even across the license fee and federal tax. Does the money of the Umsatzsteuer end up in Berlin? And a tax over a tax, how common is this? Curious minds want to know -apparently (not confirmed) European guidelines forbid taxation across taxation.

In total, the change of electricity prices for a standard German household (nominal) since 1998 looks like:

To confirm these data, I found a more recent report at BDEW also available.

This presentation shows, among others:

With the VAT raised over all components, I find the presentation of the Umsatzsteuer (VAT, abbreviated in the above table as MwSt.) somewhat deceptive in this bar graph - as it only grows proportionally because of the growth of the other constituents. But it still does the trick to show total electricity prices.

An analysis of the BDEW data suggests that since 2003 there is an increase of over 65 percent of the electricity costs for the standard German household up till 2013. In the same period, the contribution of the EEG-Umlage has increased almost twelvefold and is the component with the largest increase. In 2013, the EEG-Umlage forms nearly a fifth of total electricity costs.

Subsequently, with the rise in surcharges, the VAT has also risen: its contribution to total price nearly doubled since 2003. With a VAT at 19 percent, the VAT over the EEG-surcharge constitutes over 20 percent of the total. It remains unclear to me why a VAT should also be raised over surcharges and levies.

Crosschecking the figures of the BDEW with on-line Eurostat numbers is not straightforward: the numbers are not directly comparable. Eurostat compares a range of kWh instead of a defined amount, provides semi-annual numbers, plus the bureau switched to a different methodology after 2007. Also, I've been unable to find an overview of the evolution of the different German surcharges at Eurostat, so there can be no additional study of the price evolution of, for instance, the EEG-surcharge.

Even so, an analysis can be made for the period 2008 - 2012 and compared with the trends as derived from the BDEW. Data used are accessible here, generating the below graph.

By and large, Eurostat data confirm the trends derived from BDEW data: since 2008, the cost of German electricity for household consumers, without levies and surcharges, has only slightly increased, by nearly 10 percent. Total cost of electricity, including these, has increased by 25 percent since 2010 - this is in agreement with the claim of The Economist.

Electricity surcharges and levies (but excluding VAT) increased 63 percent since 2008. Surcharges, levies and VAT constituted 40 percent of the German electricity price in 2008, by the end of 2012 they constituted 46,5 percent - in good agreement with BDEW (in 2012: 45%).

Back to The Economist:

Energy: Tilting at windmills | The Economist

industrial power users are in a bind. As the renewables surcharge has risen, ever more companies have demanded exemptions. The number of officially "energy-intensive" firms has risen from 59 in 2003 to over 2,000 today. Between them they use around a fifth of Germany's power. Companies that do not qualify for the exemption but still use a lot of power are increasingly building their own generating capacity to avoid paying the green levy.

In total, companies forming about 18 percent of total German electric consumption are exempted of the surcharge. At first glance, this flight of German industrial consumers to dodge payment of the renewables surcharge appears problematic: the burden of the surcharge is increasingly carried by the remaining 80 percent, including household consumers, whom, all else being equal, end up paying higher prices to allow exemptions of big industrial consumers.

Digging a little deeper into the EEG, the summary of the 2013 IEA report on Germany, released May, reads and confirms:

The EEG has come under renewed criticism because of the high costs for consumers owing to the fixed FIT payments to operators of renewable power plants and a decreasing amount of chargeable energy consumption to which costs can be allocated. In February 2013, the Federal Minister of Economics and Technology and the Federal Environment Minister presented a joint proposal for a short-term amendment of the EEG to claw back the rising EEG surcharge and expressed their will to fundamentally alter the EEG in the long term.

Despite its success in attracting investment in renewable energy, the federal government has been less successful in controlling the volumes of renewable energy connecting to the system each year. The question remains, therefore, whether steering deployment volumes via a per kilowatt hour (kWh) remuneration will remain effective over the medium to long term. To date, German consumers have absorbed the costs of the EEG but the growing burden on households has ignited a political debate in Germany about the costs of the Energiewende.

And:

There is also debate regarding the allocation of the costs of the Energiewende with some arguing that household consumers carry a disproportionate share of the burden. Under existing arrangements, large consumers of electricity that use more than 10 gigawatt hours (GWh) of electricity per year pay a reduced surcharge (EUR 0.0005 per kWh) on 90% of the electricity they consume with the full surcharge payable on the remaining 10%. Electricity intensive industries that consume more than 100 GWh, and whose electricity bills represent more than 20% of total costs, may pay the lower surcharge on all of their consumption.

These large energy users also benefit from lower wholesale electricity prices brought about by the growth in renewables. Large numbers of producers, who have erected solar PV systems and connected to the distribution system, receive a revenue stream via the EEG. While these producers deliver significant benefits in terms of energy output, they also impose costs on the system, in terms of developing the distribution system and may sometimes act as a disincentive to reduce energy consumption.

In addition, the EIA calls for a reform on the additional electricity charges in Germany and asks for 'more appropriate mechanisms'. The above is also in agreement with quoted paragraph of The Economist.

However, The Economist's suggestive association of industrial electricity prices rising due to the rise of EEG-surcharge remains untested. Still, many German industrial companies are exempt from paying EEG, they profit from the current regulations. And yet, despite exemption, industrial prices of electricity have climbed steeper than the EU average?

Data to answer the initial questions posed above also remain to be parsed: the comparison between trends with households in other European nations, ditto for a comparison between industrial electricity prices. But one needs to start somewhere.

Additional commentary or corrections for improvement are welcomed.