Consider the Following Model of Demand and Supply of Coffee $Q _ { i } ^ { \text {Coffee } } = \beta _ { 1 } P _ { i } ^ { \text {Coffee } } + \beta _ { 2 } P _ { i } ^ { T e a } + u _ { i }$

Consider the following model of demand and supply of coffee: Demand: $Q _ { i } ^ { \text {Coffee } } = \beta _ { 1 } P _ { i } ^ { \text {Coffee } } + \beta _ { 2 } P _ { i } ^ { T e a } + u _ { i }$
Supply: $Q _ { i } ^ { \text {Coffee } } = \beta _ { 3 } P _ { i } ^ { \text {Coffee } } + \beta _ { 4 } P _ { i } ^ { \text {Tea } } + \beta _ { 5 }$ 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?