If a Customer discovers that services provided by you in last 2 years were extremely expensive asper market.How will you convince cust.to retain same business?

QUALITY ASPECT OF ANY PRODUCT / SERVICE HAS NO MATCH WITH ANY PRICE DIFFERENCE IN THE MARKET............ GOOD DAY

Idealy, you have convinced your partners in those2 years that the money he is spending with you is a good investment.

If that is not the case, show him benefits that he has from working with you, that competitors can´t offer him. There will always be someone doing it cheaper, so you have to do it better; and make the customer see that you´re doing it better. 

By just ensuring him that the quality of the services were also much better than the competitors in the market.

The answer depends upon the critical piece of information that is missing:  the customer's satisfaction level.  Do we want to go get heart surgery performed by the cheapest surgeon?  Do we want to hire the cheapest lawyer to handle our legal battles?  Why should it be any different in other walks of life?  There should be a reasonable correlation between the expertise provided and the skill level of the provider.  If the customer is satisfied, outline why the prices were higher than market (hopefully there is a real reason why that isn't just price gouging).  If dissatisfied, he is probably leaving anyway.

By analyzing the prices, numbers and give examples, that's probably the only way to prove you have charged him or her no more than the market price at that time.

Best to offer the customer a credit on the next transaction or contract to keep his or her business.

If the service was good and there was no downtime then there is no problem at all to convince a customer. the cost of quality of service cannot be measured by any customer but on the other hand the service provider can convince the customer about the performance of the product and the increase in the up time of the product.

In a market with high competition, if you make the price as the main comparison factor, you will always loose. Try to make the customer look at the combination of quality, service and price with the focus on quality and service. Be careful with giving him a discount, if you do so, he will see it as an admission that you were fooling him with the price. 

We are referring to the above average satisfaction level of customer, in this scenario.  

Quality has a cost 

I agree with Samuel Trapp.

The Quality of the personalized service is the main justifying point. For Other explanations convincing power is comparatively very less or inadequate. On this winning point you can very well retain the customer.  For exceptional personalized quality of service the customer complaint over the price may be a casual chat.