Consider the Following Model of Demand and Supply of Coffee $\text { Demand: } Q_{i}^{\text {Coffee }}=\beta_{1} P_{i}^{\text {Coffee }}+\beta_{2} P_{i}^{\text {Tea }}+u_{i}$

Consider the following model of demand and supply of coffee:
$\text { Demand: } Q_{i}^{\text {Coffee }}=\beta_{1} P_{i}^{\text {Coffee }}+\beta_{2} P_{i}^{\text {Tea }}+u_{i}$
$\text { Supply: } Q_{i}^{\text {Coffee }}=\beta_{3} P{ }_{i}^{\text {Coffee }}+\beta_{4} P_{i}^{\text {Tea }}+\beta_{5} \text { Weather }+v_{i}$

(variables are measure in deviations from means, so that the constant is omitted).
What are the expected signs of the various coefficients this model? Assume that the price of tea and Weather are exogenous variables. Are the coefficients in the supply equation identified? Are the coefficients in the demand equation identified? Are they overidentified? Is this result surprising given that there are more exogenous regressors in the second equation?