1. Explain the relationship between marginal cost (MC), average variable cost (AVC) and average total cost (ATC) curves. How is the shape of a rm's long-run average total cost curve related to the existence of economies/diseconomies of scale? 2. Use calculus to prove mathematically that a prot maximising rm will always minimise costs. 3. Show intuitively and prove mathematically (with calculus) that a perfectly competitive rm will not choose a quantity on the downward sloping part of the marginal cost curve. Can we conclude that the supply curve is the upward sloping part of the marginal cost curve