An economy uses two inputs to produce its output via the Cobb-Douglas production function: Q = KL, where = 0.3 and = 0.7. Its current level of inputs is K = 625 and L = 10, 000. The frm will introduce a new technology that will change the -component in its production function to = 0.350, with no change to . The economy is interested in estimating the input combination, which will keep the total output Q unchanged and the sum of inputs the same.

(iii) Using the implicit function theorem or a total diferentiation of the system, help the economy fnd the estimates of K and L around the point (K = 625, L = 10, 000, Q = 4, 352.75).