Question: 6. (Implicit function theorem without specified functional forms) A com- petitive firm maximizes its profit by choosing optimally its inputs: max pf(,1) - wl -

6. (Implicit function theorem without specified functional forms) A com- petitive firm maximizes its profit by choosing optimally its inputs: max pf(,1) - wl - rk, k.120 where f(k.1) is the production function, k is capital, I is labor, r is the rental cost of capital, w the market wage for labor and p is the output price. (a) What are the natural endogenous variables for this model? What are the exogenous variables? (b) Write the first-order conditions for optimal choices of the en- dogenous variables. (c) When can you use the implicit function theorem to determine the changes in the endogenous variables for small changes in the exogenous variables? (d) Compute the sign of changes in the endogenous variables when the exogenous variables change. 6. (Implicit function theorem without specified functional forms) A com- petitive firm maximizes its profit by choosing optimally its inputs: max pf(,1) - wl - rk, k.120 where f(k.1) is the production function, k is capital, I is labor, r is the rental cost of capital, w the market wage for labor and p is the output price. (a) What are the natural endogenous variables for this model? What are the exogenous variables? (b) Write the first-order conditions for optimal choices of the en- dogenous variables. (c) When can you use the implicit function theorem to determine the changes in the endogenous variables for small changes in the exogenous variables? (d) Compute the sign of changes in the endogenous variables when the exogenous variables change

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