Schweser Econ: q8 on Efficiency and Equity benefit, understand, quantity, question

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The question reads:
As the demand (marginal benefit) curve becomes less elastic, if the equilibrium price and quantity remain unchanged, consumer surplus:
a. decrease
b. increase
c. remains unchanged
The book answers b. Why?
As I understand, when demand curve becomes less elastic, the curve is steeper (the far end moves toward the yaxis), so the area under the curve is smaller. then the surplus should be a: decrease.
Any comments? Thanks.