True or false?

Set-up:You are interested in the effects of your own product's price on your sales. To improve the precision of your estimate of these effects you additionally include in your regression, purely as controls, several variables that measure local market demographics. You find that the demographic variables show clear signs of multicollinearity with each other, but not with your own product's price.

Conclusion:This multicollinearity biases your estimate of the effect of your own product's price on your sales, so you will need to either drop some of the controls or create composite.