Do people (under)value free stuff?
As you have mentioned, value can be conceptualized to mean different things. For the purposes of this answer lets just assume that value is measured by whether individuals are equally likely to use/chose free stuff as paid stuff - in line with the Ted talk by Esther Duflo.
Based on this assumption, I reviewed the literature and some competing narratives emerged.
First, research suggests that people actually value (i.e., choose/use) free things more than they should given the products utility - the so called zero price effect. As {1} state:
People appear to act as if zero pricing of a good not only decreases
its cost but also adds to its benefits.
They give this example:
When Ben and Jerry’s offer free ice-cream cones, or Starbucks offers
free coffee, many people spend hours in line waiting to get the free
item, which they could buy on a different day for two to three
dollars. At first glance, it might not be surprising that the demand
for a good is very high when the price is very low (zero), but the
extent of the effect is intuitively too large to be explained by this
simple economic argument.
There is a lot of additional research on this "zero price effect" which you can check out if you want (see here).
Second, research also suggests people use prices as a signals for value, and therefore will value things more highly if they are (i) more expensive or costly to procure, or (ii) more scarce. For instance in {2} Cialdini talks about how you can sometimes get people to buy more of a product by increasing the price. Additionally, some research suggests that people value things more as they invest more effort/money {3,4}. Additionally, in {2} Cialdini discusses how people generally value scarce things more highly, and things that are free, are less scarce, it appears to follow that they are not likely to be as highly valued as items one must pay for.
Third, research in developmental economics suggests that people will value products equally much when they are free/paid for. This research {e.g., 5} suggests that peoples usages of mosquito nets is not significantly, influenced by the amount of money they have to pay for them - that people are approximately as likely to use nets they got for free, and those they paid for.
I hope, that this is helpful, even if this isn't a definitive, or comprehensive answer.
References:
{1} Shampanier, K., et al. (2007). "Zero as a special price: The true value of free products." Marketing Science 26(6): 742-757.
[2] Cialdini, R. B. (2009) Influence: science and practice , 5 ed., Boston, Massachusetts: Pearson.
[3] Norton, M. I., Mochon, D. and Ariely, D. (2012) 'The IKEA effect: When labor leads to love', Journal of Consumer Psychology, 22, 453-460.
[4] Thomas, M., et al. (2004). When Do Higher Prices Increase Demand? The Dual Role of Price in Consumers’ Value Judgments.
[5] Hoffmann, V., et al. (2009). "Do Free Goods Stick to Poor Households? Experimental Evidence on Insecticide Treated Bednets." World Development 37(3): 607-617.
