Phillip runs a cost-minimising firm that creates a singular output using only two inputs. y=z1+z2. The production function is f(z1,z2)= (min(4z1,6z2))^b. where b>0 is a parameter. Input prices are w1=w2=1.

a) Phillip's long run average total cost curve increases as the quantity of output increases. What does this tell you about parameter b?

b) Graph the y-unit of output isoquant. Label any kinks or intercepts.

(c) b=1/3. Solve for the firm's long-run conditional factor demands, the long-run cost function and the long-run marginal cost function.

(d) The firm runs in a perfectly competitive market with a market price of 10. What is Phillip's profit maximising output quantity?