How do profits vary with marginal costs? Using q(p) = a - bq as the general demand function, derive the profit function as a function of a general marginal cost c. Solve for the optimal monopoly price as a function of a, b, and c. Once you have the optimal price, plug it back into the profit function. Now the profit function will depend on a, b, and c only. Now, replace a = 1 and b=0.5. With these values, plot the profit function on the vertical axis and c on the horizontal axis. How do profits vary with c? What happens if a = 2 (and b = 0.5)? What happens if a = 1 and b= 0.3? and if b = 0.7?