Consider 2 firms with the following 2 different production functions (i.) y(L,K) = aL + bK...
Consider 2 firms with the following 2 different production functions
(i.) y(L,K) = aL + bK
(ii.) y(L,K) = L^0.5K^0.5
where y denotes the quantity produced and L and K are the amount of labor and capital, respectively.
a. Assume K is fixed at 100. Do these production functions exhibit decreasing marginal products of labor?
b. Assume K can be freely chosen. Do these production functions exhibit constant returns to scale?
c. For each of the production functions, draw the isoquant associated with the output level y = 100. Assume that the rental rate for capital if 2 and the wage rate w.
d. For both of the production functions, find the optimal amount of labor and capital needed to produce quantity y = 100, as a function of the wage rate.
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