$1.$ Suppose the economy produced $2$ goods: baseballs and tennis balls. In the third quarter of

$2023($the base period$),6300$ baseballs were produced at a value of $$18$ per baseball, while

$4800$ tennis balls were produced at a value of $$6$ per tennis ball. Meanwhile, in the third

quarter of $2024,6800$ baseballs were produced at a value of $$20$ per baseball, while $5700$

tennis balls were produced at a value of $$8$ per tennis ball. $(44$ points$)$

a$.$ Solve for the nominal and real GDP in the third quarter of $2023.(11$ points$)$

b$.$ Solve for the nominal and real GDP in the third quarter of $2024.(16$ points$)$

c$.$ Solve for the growth rate of real GDP between the third quarter of $2023$ and the third quarter of $2024.$ What does this growth rate indicate or mean? In other words, what causes the real GDP value to increase? $(9$ points$)$

d$.$ Solve for the GDP price index in the third quarter of $2023$ and in the third quarter of $2024.(8$ points$)$