Question

Qd = 72 − 12P Qs = -18 + 6P

1) If price elasticity of demand for avocado at price P* is equal to -6/9, how much is P*? a) $2.00 b) $2.20 c) $2.40 d) $2.60 e) $2.80

2) What is quantity demanded at price P* at which price elasticity of demand for avocado equals -6/9? a) 42.2 tons b) 43.2 tons c) 44.2 tons d) 45.2 tons e) 46.2 tons

3) If price elasticity of supply for avocado at price P* is equal to 5/2, how much is P*? a) $2 b) $3 c) $4 d) $5 e) $6

4) What is quantity supplied at price P* at which price elasticity of supply for avocado equals 5/2? a) 6 tons b) 12 tons c) 18 tons d) 24 tons e) 30 tons

5) What is market clearing equilibrium price and quantity in Brooklyn avocado market? a) $1; 60 tons b) $2; 48 tons c) $3; 36 tons d) $4; 24 tons e) $5; 12 tons

6) What is market consumer surplus at market clearing equilibrium price and quantity in Brooklyn avocado market? a) $2000 b) $4000 c) $6000 d) $9000 e) $12000

7) What is market producer surplus at market clearing equilibrium price and quantity in Brooklyn avocado market? a) $3000 b) $6000 c) $9000 d) $12000 e) $15000

8) What is the total cost of production at market clearing equilibrium price and quantity in Brooklyn avocado market? a) $24000 3 b) $36000 c) $48000 d) $56000 e) $60000

9) What is the total revenue created at market clearing equilibrium price and quantity in Brooklyn avocado market? a) $24000 b) $36000 c) $48000 d) $56000 e) $60000

10) What is the total amount of surplus if the price of avocado is $6.00 per kg in Brooklyn avocado market? a) 6 tons b) 9 tons c) 12 tons d) 15 tons e) 18 tons 11) What is the total amount of shortage if the price of avocado is $3.00 per kg in Brooklyn avocado market? a) 12 tons b) 24 tons c) 36 tons d) 48 tons e) 72 tons

Answer 1

1) Qd = 72 - 12P , Price elasticity of demand = -(6/9) = -(2/3) = -0.666

Therefore, ∆Qd/∆P = dQd/dP = -12

Price elasticity of demand (Ed) = (∆Qd/∆P)*(P/Q) = -(6/9)

If P = $2 then Qd = 72 - 12*2 = 48

If P = $2.20 , then Qd = 72 - 12*2.20 = 45.6

If P = $2.40 , then Qd = 72 - 12*2.40 = 43.2

If P = $2.60 , then Qd = 72 - 12*2.60 = 40.8

If P = $2.80 , then Qd = 72 - 12*2.80 = 38.4

Now Elasticity at P = $2, Q = 48 is

Ed = (∆Qd/∆P)*(P/Q) = -12*(2/48) = -24/48 = -(1/2) = -0.5

Elasticity at P = $2.20 , Q = 45.6

Ed = (∆Qd/∆P)*(P/Q) = -12*(2.20/45.6) = -26.4/45.6 = -0.5789

Elasticity at P = $2.40, Q = 43.2

Ed = (∆Qd/∆P)*(P/Q) = -12*(2.40/43.2) = -28.8/43.2 = -0.666

As at P = $2.40 the elasticity is becoming - 0.666 which is the given elasticity(-6/9 = -0.666).

Therefore, P* = $2.40 (​​​​Option : c).

(2). At P* = $2.40 , Qd = 72 - 12P = 72 - 12*2.40 = 43.2

Therefore, quantity demanded at P* = $2.40 , where elasticity of demand for Avocado is -6/9 = 43.2 (Option - b) i.e 43.2 tons.

(3). Qs = -18 + 6P, Price elasticity of supply (Es) = 5/2 = 2.5

Now, at P = $2 , Qs = -6

At P = $3 , Qs = 0

At P = $4 , Qs = 6

At P = $5 , Qs = 12

At P = $6 , Qs = 18

At P = $2 , there is negative supply, so that will not be the price of supply of any quantity.

At P = $3, Qs = 0 , so we will not consider this price also to determine price elasticity of supply.

We will check the supply elasticity from P = $4 onwards.

We know price elasticity of supply (Es) = (∆Qs/∆P)*(P/Q)

Qs = - 18 + 6P

∆Qs/∆P = dQs/dP = 6

Elasticity of supply at P = $4 , Qs = 6

Es = (∆Qs/∆P)*(P/Q) = 6*(4/6) = 4.

Elasticity of supply at P = $5, Qs = 12

Es = (∆Qs/∆P)*(P/Q) = 6*(5/12) = 30/12 = 2.5.

Elasticity of supply at P = $6, Qs = 18

Es = (∆Qs/∆P)*(P/Q) = 6*(6/18) = 36/18 = 2.

Therefore, Elasticity of supply = 5/2 = 2.5 for Price = $5 (Option d). (Answer).

(4). Quantity supply at P* = $5, is Qs = -12 + 6*5 = 18 tons. (Answer option c )

(5). For market clearing price and quantity we have to equalise Qd = Qs at equilibrium.

Therefore, 72 - 12P = -18 + 6P

Or, 12P + 6P = 72 + 18

Or, 18P = 90

P = 5.

At P = $5, Q* = 72 - 12*5 = 72 - 60 = 12 tons.

Therefore, Market equilibrium price = $5 and Market equilibrium quantity is = 12 tons for avocado market.

The answer is option - (e). $5, 12 tons.

(6). Qd = 72 - 12P , it means at P = $6 , Qd = 0 , vertical intercept of demand curve is at P = $6

Equilibrium price = $5 , Quantity = 12 tons.

C.S at P = $5, and Q = 12 tons is = (1/2)*base*height

C.S = 0.5*12 tons*($6 - $5) = 0.5*12000*$1 = $6,000.

So, the answer is option (c) which is $6,000.

(7). Qs = -18 + 6P , it means at P = $3, Qs = 0 , So vertical intercept of supply curve will be at P = $3.

Producer surplus at P = $5 , and Q = 12 tons will be

P.S = (1/2)*(base)*(height)

P.S = 0.5*12 tons *($5 - $3)

P.S = 0.5*12,000*$2 = $12,000.

Therefore, P.S = $12,000. Answer is option (d).

(8). Total cost of production will be the area under the supply curve. It means area below the supply curve at P = $5 and Q = 12 tons.

[(1/2)*base*height] + [width*length]

= (1/2)*12,000*$2 + 12,000*$3

= $12,000 + $36,0000 = $48,000.

Therefore, the answer is option (c). $48,000.

(9). Total revenue at market clearing equilibrium price and quantity = P*Q = $5*12,000 = $60,000.

Therefore, the answer is option (e) $60,000.