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We measured the elastic modulus of individual multiwalled carbon nanotubes (MWCNTs) grown by catalytic chemical vapor deposition (CVD) over a broad diameter range (10-25 nm). Alternating current (ac) dielectrophoresis was used for efficient tube deposition, and atomic force microscope (AFM) force-displacement curve technique was used for stiffness measurements. The elastic modulus exhibits a strong diameter dependence, showing a difference of nearly 2 orders of magnitude in the 10-20 nm diameter range (thinner MWCNTs have higher elastic modulus). Our results support the metastable-catalyst model in which the catalyst's molten skin plays a key role.