onsider the single$-$node economic dispatch problem for a fixed demand pd:

min

p

X

g in $$G

cgpg $(1)$

s$.$t$.$ X

g in $$G

pg $$ pd $(2)$

pg $$ pg$,$g in $$G $(3)$

pg $$ pg$,$g in $$G $(4)$

$(5)$

For this problem you are welcome to use an LP solver to help you $($this is not necessary$).$

$($a$)$ Give an example of a single$-$node instance with at least $2$ generators where a

generator can benefit from misreporting cg $($while truthfully reporting pg$)$ when

prices are set according to the single$-$node economic dispatch problem.

$($b$)$ Give an example of a single$-$node instance with at least $2$ generators where a

generator can benefit from misreporting pg $($while truthfully reporting cg$)$ when

prices are set according to the single$-$node economic dispatch problem.