A bicycle is assembled out of a bicycle frame and two wheels.
a) Write down a production function of a firm that produces bicycles out of frames and wheels. No assembly is required by the firm, so labor is not an input in this case. Sketch the isoquant that shows all combinations of frames and wheels that result in producing 100 bicycles.
b) Suppose that initially the price of a frame is $100 and the price of a wheel is $50. On the graph you drew for part (a), show the choices of frames and wheels that minimize the cost of producing 100 bicycles, and draw the isocost line through the optimal basket. Then repeat the exercise if the price of a frame rises to $200, while the price of a wheel remains $50.