# How to write budget constraint if the agent sell the goods that buy

Della’s utility is $U(G,R)$

G is the consumption of gasoline per week

R is the the consumption of other goods

Just help me to write down budget constraint.

I think that

$$R*1+(G-20)*10+20*1=1000+10*X$$

where

X is the amount of the gasoline that she sell on the black market.

• Budget constraint is simply : $R+10(G-20)+20=1000$ – Amit May 3 '18 at 14:38
• @Amit but the agent also sells gasoline purchased. How can we show this in the budget constraint? Your budget constraint doesn’t tell this statement. – user315 May 3 '18 at 19:23
• @Amit then how can we find how much she consume and how much she sell? – user315 May 3 '18 at 19:24

Agent is a buyer of gasoline in the black market if his consumption of gasoline exceeds 20 i.e. $G > 20$, and he buys $(G-20)$ units from the black market in this case. So, his budget constraint is $R + 20 + 10(G-20)=100$
Likewise, agent is a seller of gasoline in the black market if his consumption of gasoline is below 20 i.e. $G \leq 20$. In this case, he sells $(20-G)$ units in the black market. So, his budget constraint is $R + 20=100 + 10(20-G)$
To conclude, his budget constraint (in all cases) is $R + 20 + 10(G-20)=100$.