The attendance (denoted by the variable F, measured in thousands of fans) at a Blue Jays home game is approximated by
F = 150W1/3 P-2/3
where W is the fraction of the games they have won so far (0 ≤ W ≤ 1) and P is the price of a general admission ticket (suppose (7 ≤ P ≤ 10) dollars).
i) Find the partial derivatives ∂F/∂W and ∂F/∂P.
ii) Suppose currently W = 0.512 and P = $8. Find the numerical value of the partial derivatives above and tell me what they mean in words.
iii) Find the partial elasticity of F with respect to P.
iv) Now suppose attendance was determined by W alone in the form of F = 150W1/3. Is this function (strictly) concave or convex? Explain. Why do you think your answer makes sense? (Be brief.)
v) Consider the equation for F given in part iv) above. Suppose W depends on the team coach's ability A in the following manner:
W = 2A1/5
Use the Chain rule to find an expression for dF/da.