"Leverage scale" does not mean to take advantage of scale; it means to take active steps to build or increase scale. In practice this involves investment directed at cost-cutting and stimulating business through efficiency, rather than direct investment in plant and equipment. The effect and purpose of doing this are to "compete cost effectively".

"Leverage
1 To use a firm's knowledge to produce a related product or service 2 Attempting to produce more without more plant or equipment
"We can leverage our new knowledge into a new line of business"
http://dictionaryofmanagementjargon.yolasite.com/#Leverage

"Leverage scale is business exec doublespeak for growing a business by adding money or some other viable stimulus to the process of making more money. It is often used in refererence to separate business ventures that join forces to cut costs, borrow more aggressively or otherwise streamline or improve their practices to achieve a mutually sought-after goal."
http://wiki.answers.com/Q/What_does_leverage_scale_mean

"P& G has four separate identifiable scale leveraging strategies:
- a retail trade strategy
- a top down Corporate vs. Division/brand funding strategy
- a consumer cohort strategy
- systemic strategies [...]
Everyone recognizes that retailers are becoming more and more powerful, demanding more price concessions from manufacturers while themselves marketing private brands of higher and higher value to consumers.
Most manufacturers respond by dumping cash into the retailer’s wallet. P&G responds by leveraging its scale. P&G is investing tens of millions of dollars in Supply Chain efficiencies to become the low-cost distributor, developing innovative distribution concepts and then “marketing” their advantages to retailers with sophisticated Activity Based Costing software tools"
http://www.reveries.com/reverb/white_papers/reveries_leverag...

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Note added at 1 hr (2013-09-02 09:20:22 GMT)
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Leveraging scale is primarily related to costs: eliminating unnecessary costs (in distribution, for example), cutting out redundant computer systems, and so on, streamlining, expanding by exploiting knowledge. That's why the emphasis in your text is on competing "cost effectively".