Question

1) Given the following equations:

   QD = 5,000 + 0.5 I + 0.2 A - 100P, and QS = -5000 + 100P

where Q is the quantity per year, P is price, I is income per household, and A is advertising expenditure.

  a.   If A = $10,000 and I = $25,000, what is the demand curve?

b.   Given the demand curve in part a., what is equilibrium price and quantity?

c.   If consumer incomes increase to $30,000, what will be the impact on equilibrium price and quantity?

2) Industry supply and demand are given by QD = 1000 - 2P and QS = 3P.

a.   What is the equilibrium price and quantity?

b.   At a price of $100, will there be a shortage or a surplus, and how large will it be?

c.   At a price of $300, will there be a shortage or a surplus, and how large will it be?

Answer 1

Answer 1a

QD = 5,000 + 0.5 I + 0.2 A - 100P

If A = $10,000 and I = $25,000, QD = 5000 + 0.5* 25000 +0.2 *10000 -100P = 5000 + 12500+2000 -100P

or, QD = 19500-100P

Answer 1b

QD = 19500-100P

QS = -5000 + 100P

At equilibrium QS=QD

Hence 19500-100P = -5000+100P

or, 100P+100P = 19500+5000

or, 200P = 24500

or, P = 24500/200 = $122.5

QD=QS = 19500-100*122.5

Q = 19500 - 12250 = 7250

Answer 1c

Now I=$30000

QD = 5000 + 0.5* 30000 +0.2 *10000 -100P = 5000 + 15000+2000 -100P

or, QD = 22000-100P

QS = -5000 + 100P

At equilibrium QS=QD

Hence 22000-100P = -5000+100P

or, 100P+100P = 22000+5000

or, 200P = 27000

or, P = 27000/200 = $135

QD=QS = 22000-100*135

Q = 22000 - 13500 = 8500

Hence both equilibrium quantity and price will increase.

Answer 2

QD = 1000 - 2P and QS = 3P.

At Equilibrium QD=Qs

hence, 1000-2P = 3P

5P = 1000

P=1000/5 = $200

QD=QS = 3*200 = 600

At Price $100, QD = 1000-2*100 =800, QS = 3*100 = 300

Hence there will be a shortage of 800-300=500 units

At Price $300, QD = 1000-2*300 =400, QS = 3*300 = 900

Hence there will be a surplus of 900-400=500 units