Why higher wages will not lead to higher prices over the long term

Many people think that if wages are increased or a minimum wage is introduced, the cost of living will rise.

This could be the immediate impact, but it will be short term. Over the long term, the cost of living will not change much. Instead, the higer cost of labor will be compensted by a lower cost of rental. The shares of the total price earned by labor, rental and profit will be adjusted, but the final price should remain almost the same.

I based my argment on logic and also on observation.

If lower wages will lead to lower cost of living, why is our cost of living so high? We do not have a minimum wage and some of the jobs pay so low that the worker cannot survive on the wages and have to do two or three jobs, or several members of the family have to work.

If wages are low, why is our cost of living so high - indeed, it is the highest in the world!

Our low wages are overwhemed by the high cost of rental, the high management salaries and the high profit margin. The prices of goods and services do not come down. Instead a larger share of the total prices paid by the buyers goes to the other components.

My logic tells me that if wages go up, then the shares earned by the other component will come down. 

Why is this simple logic not entering into the economic management of the country? The reason is that the people in power have a vested interest in pressing down wages. It allows them to enjoy higher management salaries (e.g. our government ministers earn the highest salaries in the world) and they also enjoy high rentals as property owners and high profits as shareholders. 

This means that the rich gets richer, right? Have you not heard this before?