Question

Midland Power and Light is the only seller of electricity in the area. The demand function facing the firm is   Q = 250 – 0.5P

     Where Q is quantity demanded and P is price. The firm total cost function is

     TC = 100 – 10Q + 0.5Q, and the marginal cost is MC = -10 + Q

     a/ Determine the profit-maximizing price and output rate for Midland.

     b/ Determine the cost per unit, profit per unit, and total profit.

Answer 1

a)"pure" monopolist maximizes profit under the condition that MR = MC

MR=MC=-10+Q

$P=\frac{250-Q}{0.5}=500-0.5Q$

500-0.5Q=-10+Q

510=1.5Q

Q=340

$P=500-0.5times340=500-170=330$

$Profit=340\times330-(100-100\times340+0.5\times340)=112200-(100-34000+170)=145930$

b)$profit per unit=\frac{145930}{340}=429.21$

$cost per unit=\frac{100-10\times340+0.5\times340}{340}=\frac{100-3400+170}{340}=\frac{-3130}{340}=-9.21$