Q=180√LK^0.8
L=5
K=10
1).Construct marginal product of labour and marginal product of capital
2If L=5, K=10 Measure average product of labour and average product of capital
3.return to scale production function
4.if K=5, L=10 calculate marginal rate of products.
5.law of diminishing marginal returns of labour and law of diminishing marginal returns of capital
6.how about the cross partial effect of this production function
Q=100K^0.5L^0.5.
K = 100, L = 25.
a.) The marginal product of capital and marginal product of labor are:
MPK = Q'(K) = 50L^0.5/K^0.5 = 25.
MPL = Q'(L) = 50K^0.5/L^0.5 = 100.
b.) If the price of capital was r = Rs.20 per unit, then the wage rate w is:
MPK/r = MPL/w,
25/20 = 100/w,
w = Rs.80.
C.) If r = Rs.25, then the input rate of capital K will be:
MPK/r = MPL/w,
MPK/25 = 100/80,
MPK = 31.25,
MPK = 50L^0.5/K^0.5 = 31.25,
50*5/K^0.5 = 31.25,
K = (250/31.25)^2 = 64 units.
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