$24\%)$ Farmer Boris lives for two periods. In the O$$rst period, he has $120$ bushels of wheat. If Boris consumes only a portion of the wheat in period $1,$ he can use the rest as seeds so he can harvest and consume in period $2.$ Each bushel of seeds yield $2$ bushels of wheat in period $2.$ Borisi$$utility function is u$($c$1$; c$2)=$ pc$1+0$:$5$pc$2$; where c$1$ and c$2$ are the amount of wheat $($in bushels$)$ he consumes in periods $1$ and $2$ respectively.

$(1)$ How much wheat will Boris consume in the O$$rst period and in the second period?

Suppose that a new irrigation system can double the yields $($i$.$e$.,$ each bushel of seeds planted in period $1$ yield $4$ bushels of wheat in period $2).$

$(2)$What is the maximum amount of wheat Boris is willing to give up in period $1$ in exchange for the new irrigation system?

$(3)$Borisi$$brother Christo$$ is considering giving Boris one of the two gifts:

Christo$$ pays for the irrigation system;

Christo$$ give Q bushels of wheats to Boris in period $1($assuming

Boris is not going to get the irrigation system in this case$).$

Find the value of Q such that Boris is indi$$erent between the two gifts.

$(4)$ Relate your answers to $(2)$ and $(3)$ to some measurements of welfare changes $($for example, equivalent variation, compensating variation$)$ we have studied.