Aggregate DemandConsider an economy with two goods, $1$ and $2,$ and two consumers, a and $b.$ Thepreferences of consumers are represented by the utility functions:$u^a(x_1^a,x_2^a)=2ln{x}_1^{a}3ln{x}_2^a,$ and $,u^b(x_1^b,x_2^b)=2ln{x}_1^{b}ln{x}_2^b.$Consumer a has an endowment of $20$ units of good $1($and none of good $2),$ andconsumer $b$ has an endowment of $12$ units of good $2($and none of good $1).($a$)$ Taking the relative price $=\frac{p_1}{p_2}$ as given, calculate each consumer's demandfor each of the two goods.$($b$)$ Construct the excess demand function for each good.$($c$)$ Verify that Walras' Law holds.$($d$)$ Find the Walrasian equilibrium relative price and allocation of this economy.