a. The profit-maximizing price and output are:
MR = MC,
Q = 80 - 5P, so P = 16 - 0.2Q, MR = TR'(Q) = 16 - 0.4Q,
MC = C'(Q) = 2 + Q,
16 - 0.4Q = 2 + Q,
Q = 10 units,
P = 16 - 0.2*10 = 14.
b. The size of the above profit is:
"TP = TR - C = 14*10 - (30 + 2*10 + 0.5*10^2) = 40."
c. The price elasticity of demand at the above output is:
"Ed = -b\\times P\/Q = -5\\times14\/10 = -7," so demand is elastic.
d. The marginal cost at the above output is:
MC = 2 + 10 = 12.
e. If unit costs rise by $2 at all levels of output and the firm raises its price by the same amount, its profit will decrease.
f. The profit-maximizing strategy given the above rise in costs is to decrease price to increase total revenue.
g. The firm is forgoing a huge portion of profit by raising its price $2.