$2\mathrm{.}3$ Economists estimate that the supply function for the widget market is given by

the following expression:

q $=0\mathrm{.}2\backslash$pi $40$

a$.$ Calculate the demand and price at the market equilibrium if the demand is

as defined in Problem $2\mathrm{.}2.$

b$.$ For this equilibrium, calculate the consumers$$ gross surplus, the consumers$$ net

surplus, the producers$$ revenue, the producers$$ profit and the global welfare.