1. Supply and Demand. Elasticities.
Suppose you have the following information about the supply and demand in the market:
QD = 15000 – 500*P
QS = -6000 + 3000*P
a. What is the equilibrium price and quantity?
b. What would be the combination of price and quantity at which the elasticity of demand is equal to -1?
c. Suppose the supply function changes to QS = -1000 + 3000*P. Is this an increase or decrease of supply? What is the new equilibrium price and quantity?
d. Calculate the point elasticities of supply and demand at the equilibrium prices you found in a. and c.!
To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied. Let's solve for parts (a) and (c) first:
a. Equilibrium price and quantity:
Step 1: Set QD equal to QS.
15000 - 500*P = -6000 + 3000*P
Step 2: Simplify the equation to find P.
3500*P = 21000
P = 21000/3500
P = 6
Step 3: Substitute the value of P back into either QD or QS to find the equilibrium quantity.
QD = 15000 - 500*6
QD = 15000 - 3000
QD = 12000
Therefore, the equilibrium price is 6 and the equilibrium quantity is 12000.
c. New equilibrium price and quantity after the change in supply:
Step 1: Set QD equal to the new QS.
15000 - 500*P = -1000 + 3000*P
Step 2: Simplify the equation to find P.
3500*P = 16000
P = 16000/3500
P ≈ 4.57
Step 3: Substitute the value of P into either QD or the new QS to find the new equilibrium quantity.
QD = 15000 - 500*4.57
QD = 10285
Therefore, the new equilibrium price is approximately 4.57 and the new equilibrium quantity is 10285.
Now, let's move on to parts (b) and (d) to find the combination of price and quantity at which the elasticity of demand is equal to -1, and calculate the point elasticities of supply and demand at the equilibrium prices found in parts (a) and (c).
b. Combination of price and quantity at elasticity of demand equal to -1:
To calculate the price and quantity at which the elasticity of demand is -1, we need to use the formula for elasticity of demand:
Elasticity of demand = (Percentage change in quantity demanded) / (Percentage change in price)
-1 = ((QD2 - QD1) / ((QD2 + QD1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))
Solving this equation simultaneously with the given demand function, you can find the combination of price and quantity at which the elasticity of demand is -1.
d. Point elasticities of supply and demand:
To calculate the point elasticities of supply and demand at the equilibrium prices found in parts (a) and (c), we need to use the following formula:
Price elasticity of demand = (Percentage change in quantity demanded) / (Percentage change in price)
Price elasticity of supply = (Percentage change in quantity supplied) / (Percentage change in price)
Plug in the equilibrium values from parts (a) and (c) into the respective elasticity formulas to calculate the point elasticities.