Multilevel models including random slopes: how to calculate variance In a linear mixed model, you take the covariance between data into account by adding a random intercept per cluster.
For example, you measure the effect of a drug campaign over time on students, and add a random intercept per school and a random intercept per student within a school:
$Y_{ijk}=\beta_{0}+\beta_{1}*Time+b_k+b_{jk}+\epsilon_{ijk}$
With Y the outcome variable "how much does he knows with drugs. We assume that the random intercepts are normally distributed with mean and variance: 
$b_k \sim N(0, \sigma_3^2)$, $b_{jk} \sim N(0, \sigma_2^2)$ and $\epsilon_{ijk} \sim N(0, \sigma_1^2)$
With these variances of random intercepts we can calculate the variance of the treatment effect on the different levels, for example on the school level.
But what if I want to model that the campaign has not the same average increase over time in every school? I add a random slope per school:
$Y_{ijk}=\beta_{0}+\beta_{1}*Time+b_{0k}+b_{1k}*Time+b_{jk}+\epsilon_{ijk}$
Is in this model the variation of $b_{0k}$ still meaningful? Is my intuition correct that the variation between different schools increases over time, as the random slopes drive the schools further apart? 
And as a second question, without random slope we also know that the covariance between students within the same school is given by: 
$Cov_{school}=\frac{sigma_3^2}{sigma_1^2+sigma_2^2+sigma_3^2}$
What is this covariance if a random intercept is included?
Thank you in advance!
UPDATE: included a plot of the data I am working with, level 1 are the 8 repeated measurements at each measurement occasion, level 2 are the difference measurement occasions, level 3 are the patients.

 A: I believe your intuition is correct. 
With the following model, ranging over schools $k$, individual within school $j$ and observation within individual within school $i$. (If I get your notation right).
$Y_{ijk}=\beta_0+\beta_1 t + b_{0k} + b_{1k}t + b_{jk} + ϵ_{ijk}$
With
$b_{1k} \sim N(0,\sigma_4^2)$, $b_{0k} \sim N(0,\sigma_3^2)$, $b_{jk} \sim N(0,\sigma_2^2)$, $\epsilon_{ijk} \sim N(0,\sigma_1^2)$
And assuming all random effects and error terms are pairwise independent.
Then for two two distinct individuals,$h$ and $j$, in the same school at the same time:
$\text{Cov}(Y_{ijk},Y_{ihk})=\text{Cov}(\beta_0+\beta_1 t + b_{0k} + b_{1k}t + b_{jk} + ϵ_{ijk}, \beta_0+\beta_1 t + b_{0k} + b_{1k}t + b_{hk} + ϵ_{ihk})$
$=\text{Var}(b_{0k}) + t^2 \text{Var}(b_{1k})$
So the covariance increases quadratically with time. The example in the text above looks like a correlation, but the question is about covariance. This also means the series are not stationary.
Also, to me the series in the plot look like you could argue they should be modelled with a single slope.
