Question

Suppose the market for frozen orange juice is in equilibrium at a price of $ 1.00 per can anda quantity of 4200 cans per month. Now suppose that at a price of $ 1.50 per can quantity demanded falls to 3000 cans per month and quantity supplied increases to 4500 cans per month compute the elasticity of supply for frozen orange juice between prices of $ 1.00 and $ 1.50. Explain your answer 3 points), 2 Katherine advertises to sell cookies for $ 4 a dozen. She sells 50 dozen, and decides that she can charge more. She raises the price to $ 6 a dozen and sells 40 dozen. Compute the Price elasticity of demand. Assuming that the elasticity of demand is constant how many would she sell if the price were $ 10 a box? (3 points) Timele 1

Answer 1

Since the market for orange juice is at equilibrium, it implies that Quantity demanded = quantity supplied

=> Equilibrium price, P* = $1.00, Qd* = Qs* = 4200 cans

=> when price changes to P1 = 1.50, Qd₁ = 3000 cans, Qs₁ = 4500 cans

Elasticity of supply, e* = % change in quntity supplied/ %change in price

e* = [(Qs₁ - Qs*)/Qs*]*100/[(Ps₁ - P*)/P*] *100 = [(Qs₁ - Qs*)/Qs*]/[(Ps₁ - P*)/P*]

e* = [(4500-4200)/4200]/[(1.50-1)/1] = [300/4200]/0.50 = 0.07/0.50 = 0.14

The elasticty of supply is equal to 0.14. The price elasticity of supply is inelastic has the fifty percent rise in price raises the supply by only 7%.

Katherine advertises to sell cookies for:

Price: $4, Quantity sold = 50 dozen

Price = $6, quantity sold = 40 dozen

%change in price = [(6-4)/4]*100 = [2/4]*100 = 50%

%change in quantity demanded = [(40-50)/50]*100 = [10/50]*100 = -20%

Elasticity of demand, ed* = %change in quantity demanded/ %change in price = 20/50 =- 0.4

Elasticity of demand is equal to -0.4.

If ed* = 0.4, and price changes to $10 per box,

P1 = $4, Q1 = 50 dozen

P2 = $10 , Q2 = ?

ed* = [(Q2-Q1)/Q1]/[(P2-P1)/P1]

0.4 = [(Q2- 50)/50]/ (10-4)/4] = [(Q2- 50)/50]/ 6/4] = [(Q2- 50)/50]/ 1.5]

0.4*1.5 = (Q2- 50)/50 = > 0.6 = (Q2- 50)/50 => 0.6*50 = (Q2- 50) => 30 = Q2-50

Q2 = 30+50 = 80 dozen

If elasticity is constant at 0.4, then Katherine can sell 80 dozen of cookies at $10 a box.