# 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.
– 1190
May 3 '18 at 19:23
• @Amit then how can we find how much she consume and how much she sell?
– 1190
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 $R + 20 + 10(G-20)=100$.

• Thank you sooo much. Thanks to your helps, I not only understand the answer but especially also understand how I should think when I see such type of questions. Thanks a lot. 🙏🏻
– 1190
May 5 '18 at 2:00
• Dear Amit, I hope you’re doing well. I have two questions, I solved, but I stack at some points. When you have time, I will be happy if you solve. Many thanks.
– 1190
Jul 11 '18 at 1:25
• First question economics.stackexchange.com/questions/22722/…
– 1190
Jul 11 '18 at 1:26
• Second question economics.stackexchange.com/questions/22720/…
– 1190
Jul 11 '18 at 1:26