Consider the production problem discussed in class in which 24 labor hours and 4 machine hours are to be allocated between food (x) production and wine (y) production. Suppose the production functions for x and y are as follows: Also, suppose the preferences of the agents are given by: Finally, suppose the MRT is given by where x and y denote, respectively, the aggregate quantities of food and wine produced. For each of the following allocations, determine whether they are (i) feasible and (ii) Pareto efficient. If they are inefficient, explain intuitively how it is possible to make someone betteroff without making the other person worse-off. a. ((14,2),(10,2),(5,10),(23,18)) b. ((8,2),(16,2),(5,14),(11,18)) c. ((14,2),(10,2),(14,21),(14,7))
Transcribed Image Text:Consider the production problem discussed in class in which 24 labor hours and 4 machine
hours are to be allocated between food (x) production and wine (y) production. Suppose the
production functions for x and y are as follows:
x = L°K* ,MP¸ =K*,MPg =
y= (L +4)K",MP, = K" ,MP, = (L +4)
Also, suppose the preferences of the agents are given by:
u*(x*, y“) = x"y^, MU̟ = y“,MU, = x“
u* (x*, y* ) = (x*)*y®, MU, = 3(x*)° y® , MU, = (x*)'
%3D
Finally, suppose the MRT is given by
3x
MRT(x,y) =
2y
where x and y denote, respectively, the aggregate quantities of food and wine produced.
For each of the following allocations, determine whether they are (i) feasible and (ii) Pareto
efficient. If they are inefficient, explain intuitively how it is possible to make someone better-
off without making the other person worse-off.
a. ((14,2),(10,2),(5,10),(23,18))
b. ((8,2),(16,2),(5,14),(11,18))
c. ((14,2),(10,2),(14,21),(14,7))
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