Phillip runs a cost-minimising firm that creates a singular output using only two inputs. y=x1+x2. The production function is f(x1,x2)= (min(2x1,3x2))^b. where b>0 is a parameter. Input prices are w1=w2=1.

a) Graph the y-unit of output isoquant. X2 is on the vertical axis and X1 is on the horizontal axis. Label any kinks or intercepts.

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

(c) b=1/2. 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 5. What is Phillip's profit maximising output quantity?