Question

de verse demand curve a monopoly faces is p = 110 - Q. The firm's cost curve is C(Q) = 30 +5Q. What is the profit-maximizing solution? ine profit-maximizing quantity is 52.50 (Round your answer to two decimal proces The profit-maximizing price is $ 57.50 (round your answer to two decimal places.) What is the firm's economic profit? The firm earns a profit of $ 2726.25 (round your answer to two decimal places.) How does your answer change if C(q) = 100 +5Q? The increase in fixed cost A. causes the firm to increase both the price and quantity, and profit increases. B. has no effect on the equilibrium price and quantity, but profit will decrease. c. has no effect on the equilibrium quantity, but the equilibrium price increases and profit increases. D. has no effect on the equilibrium quantity, but the equilibrium price increases and pront decreases. YOU ANSWERED: 0

show all work please

Answer 1

TR = PRICE * QUANTITY

= {110- Q}*Q

= 110Q - Q²

MR = 110 - 2Q [ by differentiating TR, we get MR]

TC = 30 +5Q

MC = 5 [ by differentiating TC, we get MC]

Equilibrium is determined when MR= MC

110 -2Q =5

105 = 2Q

Q = 105/2

= 52.5 . Hence, profit maximising quantity is 52.5

Substituting 52.5 in price function, we get profit maximising price

P = 110-52.5

= 57.5. Hence, profit maximising price is 57.5

Economic profit = REVENUE - COST

=[ 110*52.5 - 52.5^2] - [30 +5*52.5]

=[ 5775 -2756.25] - [30+ 262.5]

=[3018.75] - [292.5]

= 2726.25

WHEN COST = 100 +5Q

MR = 5 [ no change in MR]

At equilibrium, MR =MC

110-2Q = 5

Q = 52.50 [ QUANTITY DOES NOT CHANGE]

Since quantity remains same, equilibrium price also remains same.

profit = revenue - cost

= 3018.5 - [100 + 5*52.5]

= 3018.5 - 362.5

= 2656 [ profits got decreased with an increase in fixed cost]

Hence, increase in fixed cost has no effect in equilibrium price and quantity but profit will decrease.