Consider static general equilibrium. A representative consumer has preferences as follows: u$($c$,`)=($c$$c$)$ $`$ where c represents a minimum level of consumption $($e$.$g$.$ food or subsistence level of consumption$)$ and and in $(0,1)$ are constants and $`$ is leisure. There is no government or taxes and $$ is the profit coming from firms that are owned by consumers and households. If $1$ is the normalised total hours in the day then $(1`)$ is the labour supply. The representative firm has a technology $($with A $>$ c$)$ which depends on labour inputs alone n and A measures technological progress: Y $=$ An $($a$)$ Find the budget constraint for this economy and the labour supply. $($b$)$ Find the expression for the equilibrium wage and labour in this economy. $($c$)$ How does labour supply change if $($i$)$ c increases or $($ii$)$ A $($knowledge or efficiency of labour$)$ increases? How do you interpret these results?