Question

Assume that the supply function for X is Q(s) = -50 + 5P.

Using this information, select the correct responses from the answers below. Note that multiple answers may be correct.

A.)

The inverse supply function can be written as: P = 10 + 1/5Q(s) while the supply function is equal to Q(s) = -50 + 5P. This means that the y-intercept for the inverse supply function is -50.

B.)

When the market price is equal to 50, the following statements are correct: Quantity supplied is equal to 200. Total revenue is equal to 10,000. Producer surplus is equal to 4,000

C.)

When the market price increases from 60 to 70, the following statements are correct Quantity supplied increases from 250 to 300 Total revenue increases from 15,000 to 21,000 Producer surplus increases from 6,250 to 9,000

D.)

When the market price declines from 40 to 30, the following statements are correct Quantity supplied falls from 150 to 100. Total revenue falls from 6,000 to 3,000. Producer surplus rises from 2,500 to 4,000.

E.)

The law of supply states that price and quantity supplied are positively related, that is, as price increases, quantity supplied increases. The law of supply reflects the law of increasing marginal returns, that is, as production increases, the marginal cost of production falls, thus price increases are necessary to increase profitability.

Answer 1

Q(s) = -50 + 5P
So, 5P = Qs + 50
So, P = (50/5) + (1/5)Qs
So, P = 10 + (1/5)Qs

Vertical intercept (when Q = 0) is P = 10

Producer surplus = (1/2)*(given P - minimum Price)*Qs = (1/2)*(P - 10)*Q

When P = 50,
Q = -50 + 5P = -50 + 5(50) = -50 + 250 = 200
Total Revenue = P*Q = (50)*(200) = 10,000
Producer surplus = (1/2)*(50-10)*200 = 4000

When P = 60,
Q = -50 + 5P = -50 + 5(60) = -50 + 300 = 250
Total Revenue = P*Q = (60)*(250) = 15,000
Producer surplus = (1/2)*(60-10)*250 = 6250

When P = 70,
Q = -50 + 5P = -50 + 5(70) = -50 + 350 = 300
Total Revenue = P*Q = (70)*(300) = 21,000
Producer surplus = (1/2)*(70-10)*300 = 9000

When P = 30,
Q = -50 + 5P = -50 + 5(30) = -50 + 150 = 100
Total Revenue = P*Q = (30)*(100) = 3,000
Producer surplus = (1/2)*(30-10)*100 = 1000

When P = 40,
Q = -50 + 5P = -50 + 5(40) = -50 + 200 = 150
Total Revenue = P*Q = (40)*(150) = 6,000
Producer surplus = (1/2)*(40-10)*150 = 2250

So, correct statements are: B and C