Robinson Cruse obtains utility from the quantity of fish he consumes in one day

ID: 1176534 • Letter: R

Question

(F), the quantity of coconuts he consumes that day ( C), and the hours of leisure time he has

during the day (H) according to the utility function:

Utility = U(F, C, H) = (F^1/4)(C^1/4)(H^1/2)

Robinson%u2019s production of fish is given by

F = sqrt(LF),

where LF is the hours he spends fishing; and his production of coconuts is determined by

F = sqrt(LC),

where LC is the hours he spends picking coconuts. Assume that Robinson decides to work an

eight-hour day (i.e., H = 16), graph his production possibility frontier for fish and coconuts.

Show his optimal choices of those goods.

Hint: By the symmetry between F and C, his optimal choices must be equal

To maximise the utility H =16, F = 4, C = 4

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