Based on the Homework $1,$ please answer the following questions.

$(1)$ Based on MRSG$2$G$1,$ optimal combination of two products occurs at G $1=\_\_\_\_\_\_\_$ and G $2=\_\_\_\_\_\_\_\_\_\_,$ because IPR$=\_\_\_\_\_\_\_.$

$($Please calculate the IPR here$).$

$(2)$ Based on the information that you get, can you mathematically and graphically $($by finding the two end points$)$ derive the budget

line $($TB$)?$

$(2)$ If the price of cigarettes $($PG$2)$ increases to $$1\mathrm{.}75$ per pack and PG$1$ remains unchanged, optimal combination of two products will

change to G $1=\_\_\_\_\_$ and G$2=\_\_\_\_\_\_,$ because IPR$=\_\_\_\_\_\_\_\_\_\_\_\_\_\_($ based on MRS G$2$G$1).$ This is because cigarettes become

relatively $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ comparing to the price of beer, and consumer would prefer $\_\_\_\_\_\_\_$ cigarettes.

$(3)$ If the price of cigarettes $($PG$2)$ decreases to $$0\mathrm{.}75$ per pack and PG$1$ remain unchanged, optimal combination of two products will

change to G $1=\_\_\_\_\_$ and G$2=\_\_\_\_\_\_,$ because IPR$=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_($ based on MRS G$2$G$1).$ This is because cigarettes become

relatively $\_\_\_\_\_\_\_\_\_\_\_\_$ comparing to the price of beer, and consumer would prefer $\_\_\_\_\_\_\_$ cigarettes.