Question

Your firm has estimated the following inverse demand curve for the market in which your firm operates:

P = 600 - 1/3Q(d)

The prevailing market price is currently $100 a unit.

Determine which of the following statements are correct (multiple statements may be correct).

		A.) When price is equal to $700 a unit, quantity demanded is equal to -300.
		B.) At a prevailing market price of $100 a unit, consumer surplus is equal to $375,000 and consumer expenditure would be $150,000.
		C.) If the price rises from $100 to $200 a unit, the resulting consumer surplus at $200 a unit would be $375,000
		D.) At $100 a unit, consumer surplus is equal to $150,000.
		E.) If the price rises from $100 to $200 a unit, the resulting consumer surplus at $200 a unit would be $240,000
		F.) At $100 a unit, consumer expenditure is equal to $150,000.

Answer 1

P = 700 = 600 - 1/3Q(d)
So, (1/3)Q = 600-700 = -100
So, Qd = -100*(3) = -300

Maximum P possible (when Q = 0) = 600
Consumer surplus = (1/2)*(Maximum P - Given P)*Qd = (1/2)*(600-P)*Qd

When P = 100 = 600 - 1/3Q(d)
So, (1/3)Q = 600-100 = 500
So, Qd = 500*(3) = 1500)

Consumer surplus = (1/2)*(600-100)*(1500) = $375,000
Consumer spending = P*Qd = 100*(1500) = $150,000

When P = 200 = 600 - 1/3Q(d)
So, (1/3)Q = 600-200 = 400
So, Qd = 400*(3) = 1200)

Consumer surplus = (1/2)*(600-200)*(1200) = $240,000
Consumer spending = P*Qd = 200*(1200) = $240,000

So, the correct statements are:

A.) When price is equal to $700 a unit, quantity demanded is equal to -300.
B.) At a prevailing market price of $100 a unit, consumer surplus is equal to $375,000 and consumer expenditure would be $150,000.
E.) If the price rises from $100 to $200 a unit, the resulting consumer surplus at $200 a unit would be $240,000
​​​​​​​F.) At $100 a unit, consumer expenditure is equal to $150,000.