Assume production function, Y = (2L (3/4))(4K(1/4)). Cost function, C = wL+rK (where w=wage rate & r=cost of capital).
i) Using Lagrangian technique, find out the Least Cost of the production. First, describe the Objective function and Constraint. Second, find out the solution for the optimal units of the labour and capital, L* and K*.
Note: throughout solution, don’t use values given in (ii)
ii) If w = $5/hr; capital cost, r = $10/hr, what is the cost of the producing Y = 200.
iii) For the similar problem, find out the optimal units of the Labour (L*) and Capital (K*) which will maximize Profit.