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Reducing food wastage should in theory reduce demand for food, thereby driving food prices down. However, there are a lot more factors involved here (for example, the reduction in price of a product x due to lesser wastage in region A may not actually lead to lesser prices in region B because transportation costs may fully offset the price decrease).
Has there been a study that quantitatively links food wastage and food prices?
As far as I know, there are no economic studies studying the effect of food waste on food prices. In part, this may be due to difficulties in measuring food waste, as noted by a commenter. However, a more fundamental difficulty stems from a lack of 'exogenous' variation in food waste. The amount of food waste may vary significantly between places and times, but so do other factors (taxes, technology, consumer demand) which also influence the price of food.
In light of the lack of empirical studies on this topic, allow me to discuss it from a more theoretical point of view. You write
Reducing food wastage should in theory reduce demand for food, thereby driving food prices down.
There are therefore two questions here:
In my view, the answers are 'yes' and 'maybe, maybe not'. Let me address these questions in turn.
Question 1
Alecos has produced an interesting argument as to why a reduction in food waste could have no effect (or even increase) demand for food. Essentially, he models a reduction in food waste as an exogenous decrease in the price of food. When the price of food falls, we consume more of it. However, for a given level of consumption, our demand for food falls. With logarithmic utility, these factors cancel out; but in principle, either factor could be more important (so food demand could increase or decrease).
While this is an intriguing argument, I find it rather unconvincing. First, many people cut back on food waste precisely to reduce the amount of food they buy. It would be perverse to claim that such people 'respond' to their reduction in food waste by buying more food. Second, in modern economies, people are already satisfying (and often exceeding) their calorific requirements. Hence, the binding constraint on the quantity (not necessarily quality) of food purchased is how much food they want to eat, not the amount of food they waste. Third, as a modelling choice, I think we should view 'food waste' as an active choice which consumers make as opposed to some parameter to which consumers optimally react. I doubt that Alecos' conclusion would hold once recognise that wasting food is a choice, though of course we could check this.
In my view, things are more simple. If people waste less food, their consumption of food will not significantly change. As a result, their demand for food must fall.
Question 2
However, I am not so confident that a fall in demand will lead to a fall in prices. To simplify, let us suppose that food is produced by identical perfectly competitive suppliers in a market with free entry. In that case, it can be shown that each producer will produce at the level that minimises their average cost; and that the market price will equal this average cost. Hence, the market price does not depend on demand.
Naturally, this is just market structure and it may be useful to think about others (e.g. oligopoly). However, I think that you will find that the effect of demand on prices is often ambiguous and depends on the economies of scale that are present in the industry.
Reducing food wastage should in theory reduce demand for food
Let's examine this claim in a simple static framework. Assume preferences over two goods like
$$U(x_1,x_2) = a\ln x_1 + (1-a)\ln x_2 \tag{1}$$
where $x_1$ is food and subject to waste, while $x_2$ is not subject to waste. Now, the quantity in the utility function is not the quantity purchased but the quantity actually consumed. Waste appears in the budget constraint as, say, a mark up in the quantity that is desired to be consumed,
$$p_1\cdot(1+d)x_1^c + p_2x_2 = I, \;\;\;d\geq 0$$
In order for the consumer to consume $x_1^c$, it must purchase $x_1^d=(1+d)x_1^c$ quantity due to waste.
The Lagrangean here is
$$\Lambda = a\ln x_1^c + (1-a)\ln x_2 + \lambda \Big[I-p_1\cdot(1+d)x_1^c - p_2x_2\Big]$$
The first order condtions are
$$\frac a {x_1^c} = \lambda p_1(1+d),\;\;\; \frac {1-a} {x_2} = \lambda p_2$$
From which we obtain $\lambda = 1/I$ and so the demand function for food
$$x_1^c(1+d) = \frac a {p_1}I$$
Note carefully that "desired quantity to be consumed" is not determined independently from the waste factor.
Summing over all $N$ identical consumers,
$$X_1^d = X_1^c (1+d) = N\cdot \frac a {p_1} I$$
It is the right-hand-side that expresses the market demand curve in a price-quantity graph -and in it, food waste does not appear.
Assume that the waste factor is reduced to $d' < d$, without this affecting the supply curve. It follows that the demand curve will not be affected either, and so neither the equilibrium price: what will happen is that consumers will continue to demand/purchase the same quantity, but they will now consume more of the good, since waste has somehow been reduced.
We see that the OP's argument that reduction in food waste will lead to a shift in the demand curve, rests on a crucial and implicit assumption: that the amount consumed given current waste, is a point of satiation, namely that consumers consume "all they want" irrespective of prices and income, and so if waste is reduced, they will not want to increase their actual consumption, and so they will demand/purchase less since the dead-burden of waste has been reduced.
For people that do not go hungry, there may indeed be the impression that they actually consume at their point of satiation. But this is not at all certain.
Sometime back, I remember reading about a new coating material that could reduce all friction from glass or plastic. One possible consequence? Bottles of sauce (like tomato ketchup, mayonnaise etc) if coated with this material, would totally and easily empty down to the very last drop. Are we sure that this would mean that the consumers would end up buying less bottles because each bottle would now "last longer"? Or they would end up eating a little more sauce per meal?
