Homework Assignment 7 Suppose that the output q of a firm depends on the quantities of z1 and z2 that it employs as inputs. Its output level is determined by the production function 1. q = 26z1 + 24z2 7z2 1 12z1z2 6z2 2 2. Write down the firm's profit function when the price of q is $1 and the factor prices are w1 and w2(per unit) respectively. 3. Find the levels of z 1 and z 2 which maximize the firm's profits. Note that these are the firm's demand curves for the two inputs. 4. Verify that your solution to [2] satisfies the second order conditions for a maximum. 5. What will be the effect of an increase in w1 on the firm's use of each input and on its output q? [hint: You do not have to explicitly determine the firm's supply curve of output to determine q/w1. Instead write out the total derivative of q and make use of the very simple expressions for q/z1 and q/z2 at the optimum that can be obtained from the first order conditions.] 6. Is the firm's production function strictly concave? Explain