Robinson is trapped on an island and can produce Fish (F) or Coconuts (C) with his time. Let $ L_F $ and $ L_C $ denote labor hours dedicated to fishing or gathering coconuts, respectively.Robinson's technological relationships for producing fish is given by:\[ F = \frac{1}{2} \sqrt{L_F} \]Robinson's technological relationships for producing coconuts is given by:\[ C = \frac{1}{4} \sqrt{L_C} \]Which of the following will be true regarding Robinson's PPF? (hint: a well-drawn picture will help)- ⬜ it will exhibit increasing opportunity cost with respect to both goods- ⬜ it will exhibit decreasing opportunity cost with respect to both goods- ⬜ not enough information provided to make an assessment- ⬜ it will exhibit constant opportunity cost with respect to both goods

Robinson's production technology for fish production is and production technology for coconut…

Answered: Robinson is trapped on an island and…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Robinson is trapped on an island and can produce Fish (F) or Coconuts (C) with his time. Let $ L_F $ and $ L_C $ denote labor hours dedicated to fishing or gathering coconuts, respectively.

Robinson's technological relationships for producing fish is given by:

\[ F = \frac{1}{2} \sqrt{L_F} \]

Robinson's technological relationships for producing coconuts is given by:

\[ C = \frac{1}{4} \sqrt{L_C} \]

Which of the following will be true regarding Robinson's PPF? (hint: a well-drawn picture will help)

- ⬜ it will exhibit increasing opportunity cost with respect to both goods
- ⬜ it will exhibit decreasing opportunity cost with respect to both goods
- ⬜ not enough information provided to make an assessment
- ⬜ it will exhibit constant opportunity cost with respect to both goods

Expert Solution

Step 1: Determine the given information:

Robinson's production technology for fish production is $F equals 1 half square root of L subscript F end root$

and production technology for coconut production is $C equals 1 fourth square root of L subscript C end root$

Here L_F and L_C denote the labor hours dedicated to fishing and gathering coconuts.

Production possibility frontier (PPF) is a curve that represents the maximum combination of two goods produced by a firm/country/individuals with available resources and technology. It represents the tradeoff that an individual/firm/country faces while allocating resources in the production of two goods.

The shape of the PPF reveals the opportunity cost of producing fish in terms of coconuts. If the PPF is bowled outward or concave then the PPF will exhibit increasing opportunity cost with respect to both goods.

If the PPF is bowled inward or convex then the PPF will exhibit decreasing opportunity cost with respect to both goods.

If the PPF is a straight line then the PPF will exhibit constant opportunity cost with respect to both goods.

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