Only part 2 (a) plz 2(a) Robinson\'s technology for producing coconuts (x) is re

Question

Only part 2 (a) plz

2(a) Robinson's technology for producing coconuts (x) is represented by x = V , where l is labour, in hours per day. His preferences for coconuts and labour are given by the utility function u(l,x)xAssume Robinson is the only consumer of coconuts, and the owner of the only firm that produces coconuts. Suppose the price of coconuts is set at 1 The Pareto efficient allocation of labour and coconut is GarIkd x UESTION 4 2-(b) In the competitive equilibrium of this economy, Robinson's consumption of coconuts is his labour supply is the market wage rate is and the firm's profit is If your answer is a fraction, convert to a decimal.

Explanation / Answer

a. x = l^0.5

Simply put above relation in utility function –

U = l^0.5 – l/2

To calculate pareto efficient solution, we may maximize above utility function with respect to l and put first derivative = 0.

dU/dl = 0.5/l^0.5 - ½ = 0
or, 1/l^0.5 = 1
1/l = 1
l =1.

If l = 1 then x = 1^0.5 = 1

Then pareto efficient allocation l = 1 and x =1.

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