In their paper Effect of oil spills on fish production on the Niger Delta, Eze Simpson Osuagwu and Eseoghene Olafia "examine the effects of oil spills on fish production in the Niger Delta of Nigeria from 1981-2015" using the following variation of the Cobb-Douglas production function:

Ft=ASt¹Pt ²Ct ³Lt ⁴

where Ft is fish production as captured fish measured in tones at period t, A is total-factor productivity, St is the quantity of oil spills in barrels at period t, Pt is oil production in barrels at period t, Ct is fish capital, proxied by number of fishery loans at period t, and Lt is fish labor captured by the number of fishers at period t.

(a) analyze (i)the production function given above and (ii) your derived growth accounting form of the production function to determine whether the coefficient 1 is more likely to be positive, negative, or zero.

(b) Derive the relationship between the s that must hold if this production function displays constant returns to scale.