Skateboards must be produced with exactly 4 wheels and 1 board for each skateboard. (Suppose that no assembly is required, so labor is not an input.) Let Q be the number of skateboards, W be the number of wheels, and B be the number of boards. The price of a wheel is PW and the price of a board is PB.
(a) Write down the production function for skateboards, Q(W,B).
(b) Derive the long-run total cost function for producing skateboards, TC(Q,PW, PB).
(c) Draw a graph of the demand curve for wheels if the firm wants to produce 100 skateboards.
(d) On an optimal choice diagram with W on the horizontal axis and B on the vertical axis, draw the isoquant for Q = 100 and indicate the optimal choices of W and B on that isoquant. Now use this same diagram to illustrate the expansion path.