Robinson Crusoe's preferences over coconut consumption, C, and leisure, R, are represented by the utility function U(C, R) = CR. There are 48 hours available for Robinson to allocate between labor and leisure. If he works L hours, he will produce the square root of L of coconuts. He will choose to work

Question

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Robinson's utility function is U(C,R) = CR, so he wants to maximize the product of his coconut consumption and leisure time.

His coconut consumption is determined by how many hours he works. If he works L hours, he will produce the square root of L of coconuts.

His leisure time is equal to 48 - L hours.

To maximize his utility, Robinson must choose the number of hours worked that maximizes the product of his coconut consumption and leisure time.

Mathematically, we can express this as:

max(C * (48 - L)) = max(sqrt(L) * (48 - L))

We can simplify this expression by taking the derivative with respect to L and setting it equal to zero:

d/dL (sqrt(L) * (48 - L)) = 24 - 3L/sqrt(L) = 0

Solving for L, we get L = 16.

Therefore, Robinson will choose to work 16 hours to maximize his utility.

Robinson Crusoe's Preferences Over Coconut Consumption, C, and Leisure, R