3. The demand for food purchased 1n grocery stores is given by DG = 100 Pg+ 2PT where Pg' 15 the price (index) of food in supermarkets and PT 15 the price of takeouts. Correspondingly, the demand for takeouts ls DT 100 PT + %.PG The supply functions are given by SG 1PG and ST PT respectively The government imposes the tax of 420 on takeout food. Determine how the incidence of this tax is split between consumers and producers of the two types of food. Note: you have to nd prices for both goods that yield an equilibrium in both markets at the some time