Question

Quantity demanded price quantity supplied 45 $10 77 50 8 73 56 6 68 61 4 61 67 2 57 refer to the data. suppose quantity demanded increased by 12 units at each price, changing the equilibrium price in a direction and an amount for you to determine. over that price range, supply is multiple choice perfectly elastic. perfectly inelastic. elastic. inelastic.

Answer 1

a. When the demand increases by 12 units, the equilibrium price rises to $6.2093 and the equilibrium quantity rises to 67.7442 units.

b. The price elasticity of supply (PES) at equilibrium is 0.20. Since the price elasticity is less than 1, we conclude that supply is inelastic.

From the given data, we can see that the equilibrium price is $4 and the equilibrium quantity is 68 units.

If the demand increases by 12 units at each point of price decline, the demand equation will be :

$Qd = 105 - 6P$

and the supply equation will be:

$Qs = 51.6 + 2.6P$

Since Quantity demanded and supplied are equal at equilibrium, we can equate the demand and supply equations and solve for price (P). Equating the two equations above, we get,

$105-6P = 51.6 +2.6P$

$53.4 = 8.6P$

P = $6.2093

Substituting the value of P in the demand equation, we get,

$Qd = 105 - (6*6.2093)$

$Qd = 105 - 6P$

$Qd = 67.7442$ units

b. Calculation of Price Elasticity of supply at equilibrium level.

P₀ = $4

Q₀ = 61

P₁ = $6.2093

Q₁ = 67.7442

$% change in quantity = [ (Q_1 - Q_0) / Q_0 ] * 100$

% change in quantity = 11.05607%

$% change in price = [ (P_1 - P_0) / P_0 ] * 100$

% change in price = 55.2325%

Price Elasticity of Supply (PES):

$PES = % change in quantity / % change in price$

PES = 11.05607% / 55.2325%

PES = 0.20