Can mixed models can be used to study longitudinal changes in independent variable? I have a R dataframe that contains prices and many metadata fields from books published between 1700 and 1800:
df <- read.table("https://raw.githubusercontent.com/duhaime/mixed-model-book-prices/master/data/clustered_estc_price_data.txt", 
                 sep="\t", 
                 quote='"',
                 fill=NA,
                 na.strings='NULL',
                 colClasses = c('character','numeric','character','numeric','character', 'numeric',
                                rep('character',3), rep('numeric',3), rep('character',2), rep('numeric',3), 'character')
)

colnames(df) <- c("estc_id","year","raw_size","clean_size","raw_pages","clean_pages","notes","raw_price","parsed_price","farthings","illustrations","farthings_per_page","author","title","ignore","cluster","unique_years_in_cluster","canonical_title")

Using this data, I wish to evaluate whether scholars were right to argue that book prices "tended to drop" after 1774. (Their claim is that the creation of fixed-term copyright in 1774 created open-source books which increased the supply and decreased the demand for classic works like those of Shakespeare and Homer.)
Some great statistical consultants at my university suggested that mixed models would be an appropriate strategy in this case because I have grouped observations (many prices pertain to the same book, many books were written by the same author, many authors were published by the same publisher, etc.) Using the lme4 package in R, I built a simple mixed model that treats the number of pages, book size, and the presence or absence of illustrations as fixed effects, and the particular title of a work as well as the year in which a work was published as mixed effects:
price.model = lmer(farthings ~ clean_pages + clean_size + as.factor(illustrations) + 
                     (1|cluster) + (1|year), data=df)

I'm still learning about mixed models, but at this point am not sure whether I will be able to use the model above to pursue my question. 
Are mixed models an appropriate strategy for studying the degree to which book prices sank after 1774? Would a piecewise mixed model be more appropriate? I would be entirely grateful for any assistance others can offer with this question. 
 A: If you are looking at a question like "book prices tended to drop after 1774" then, as far as I can see, book price is your dependent variable and mixed models would be appropriate. 
Indeed, in the model that you have written, "farthings" (which I assume is a measure of price) is the dependent variable.
If you are asking whether the independent variables in a mixed model can vary over time, the answer is "yes". 
You have a fairly complicated model here, with many groupings - there are both repeated measures and clusters.  It can still be modeled, but it's a tricky one to use as your introduction to these models.  
A: I think your model is perfectly fine for your question.
If you are new to the lme4 package, then perhaps you need some advice on how to extract the relevant estimates from your fitted model object price.model. To extract the random effects for years, use ranef(); to get the variances as well, include condVar = TRUE
my.ranef.year <- ranef(price.model, whichel = "year", condVar = TRUE)

my.ranef.year is a data.frame with only one column, called "(Intercept)". To get the point-estimates for each year:
year.effect <- my.ranef.year[['year']]$'(Intercept)'

To get the standard errors:
std.err <- sqrt(attr(my.ranef.year[['year']], which = "postVar")[,,])

95% Confidence intervals:
lower.bounds <- year.effect - 1.96 * std.err
upper.bounds <- year.effect + 1.96 * std.err

To plot these (using the package gplots):
library(gplots)
plotCI(as.numeric(rownames(my.ranef.year[['year']])), y = year.effect, li = lower.bounds, ui = upper.bounds, xlab = "years")


I am not an economist, but I think you should try to control for Inflation by adding a fixed term that reflects the consumer price index for the period you are studying.
