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13 Nov 2019
A production function P is given by P-f(I, k) = 0.4812-0.0213 + 1.8k2-012k3 where / and k are the amounts of labor and capital, respectively, and P is the quantity of output produced. Find the values of and k that maximize P. Solution: To find the critical points we need to solve the system Pi The first equation gives thatl This implies that there are four critical points (0,0), (0, and Pk . From the second equation we get k- ,0), and ( Submit Answer Tries 0/8 To apply the second-derivative test we need to find the second partial derivatives of P We find that Pu- , and Pk,- lk Therefore Submit Answer Tries 0/8 Next we apply the second-derivative test to each critical point. At (0,0), we have that D(0,0) and Piz(0, 0) v . Therefore there is at (0,0) Submit Answer Tries 0/8 At (0, ) we have that D(0, v . By the second-derivative test there is at (0 Submit Answer Tries 0/8 At ,0) we have that D v. By the second-derivative test there is v at 0 Submit Answer Tries 0/8 Because D( second-derivative test there is and Pr( v at this point. by the The maximim output is obtained whent and k
A production function P is given by P-f(I, k) = 0.4812-0.0213 + 1.8k2-012k3 where / and k are the amounts of labor and capital, respectively, and P is the quantity of output produced. Find the values of and k that maximize P. Solution: To find the critical points we need to solve the system Pi The first equation gives thatl This implies that there are four critical points (0,0), (0, and Pk . From the second equation we get k- ,0), and ( Submit Answer Tries 0/8 To apply the second-derivative test we need to find the second partial derivatives of P We find that Pu- , and Pk,- lk Therefore Submit Answer Tries 0/8 Next we apply the second-derivative test to each critical point. At (0,0), we have that D(0,0) and Piz(0, 0) v . Therefore there is at (0,0) Submit Answer Tries 0/8 At (0, ) we have that D(0, v . By the second-derivative test there is at (0 Submit Answer Tries 0/8 At ,0) we have that D v. By the second-derivative test there is v at 0 Submit Answer Tries 0/8 Because D( second-derivative test there is and Pr( v at this point. by the The maximim output is obtained whent and k
Trinidad TremblayLv2
27 May 2019