1 1 A seller has the production function f(x, y) = x+ + y4. Yes, that is x to the power 4 plus y to the power 4. Denote the output by z. (a) (2 marks) Fix x = 16. Find the cost function C(z) as a function of the prices px and py of x and y. (b) (1 mark) Use your cost function from part (a) to find the supply function for a seller with this production function in a competitive market. (c) (3 marks) Suppose now that both inputs are variable. Find the cost minimizing bundle of inputs as a function of the level of output z and the prices of the inputs. (d) (1 marks) Does this production function have decreasing returns to scale? Explain.