The aggregate demand for gasoline in the city of Cambridge is given byD=20020P

and the aggregate gasoline supply isS=60P

, whereP

is the price of gasoline and quantities are measured in gallons. To help tackle the issues of climate change, the city sets a bold goal to reduce aggregate gasoline consumption to 80% of its current level.

As a student taking 14.100x, you are asked to help the city of Cambridge come up with a good policy plan in order to achieve this goal. At the same time, you are also concerned about how you will be affected by any new policy since gasoline is in your consumption bundle. For simplicity, let's call all the remaining goods in your consumption "all other goods" (A

). Your utility from gasoline (G

) and all other goods (A

) isU(A,G)=A

G

. The price of all other goods is $10/unit and your income is $100.

A tax policy can achieve the goal of reducing gas consumption to 80% of the equilibrium level found in the first question. Suppose the City makes the suppliers pay a tax ofT

dollars for each gallon of gas they sell. What size shouldT

be in order to meet the City's target?

MRS=MUAMUG=GA=PAPG=MRT.

T =