Suppose a perfectly competitive firm's short run total cost function is TC(Q) = 12 +6Q - 3Q² +Q³. (a) Determine an expression for each of the firm's short run marginal cost curve MC, short run average total cost curve ATC and short run average variable cost curve AVC. Draw all of the MC, ATC and AVC curves into one figure. (b) Analytically derive a formula for the firm's short run supply curve S. Plot S into your figure from part (a). (c) Suppose that p = 6. (1) What quantity Q does the firm produce if it maximizes profit? (2) What profit does the firm make? Illustrate this profit in your figure from part (a). (3) Which profit would the firm make if it would shut down? Illustrate this profit in your figure from part (a).