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Given demand and supply functions Qd = 20 − 2p and Qs = 10 + 3p, determine the equilibrium price and quantity and calculate the point price elasticity of demand at equilibrium.
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3 partsStep-by-step solution
7 stepsHere are the solutions to the demand and supply functions problem:
Given the demand and supply functions:
Demand function:
Supply function:
where is price in cedis and is quantity in kilos.
Part i· 3 steps
Determine the equilibrium price and quantity
Set demand equal to supply to find the equilibrium price.
At equilibrium, .
Solve for .
The equilibrium price is GH¢2.
Substitute the equilibrium price into either the demand or supply function to find the equilibrium quantity.
Using the demand function:
Using the supply function (to verify):
The equilibrium quantity is 16 kilos.
The equilibrium price is and the equilibrium quantity is .
Part ii-0.25
Calculate point price elasticity of demand at equilibrium
The formula for point price elasticity of demand () is:
Find the derivative of the demand function with respect to price ().
Given , the derivative is the coefficient of .
Substitute the values of , equilibrium price (), and equilibrium quantity () into the elasticity formula.
Equilibrium
EquilibriumThe point price elasticity of demand at equilibrium is .
Part iii0.375
Calculate the price elasticity of supply at equilibrium.
The formula for point price elasticity of supply () is:
Find the derivative of the supply function with respect to price ().
Given , the derivative is the coefficient of .
Substitute the values of , equilibrium price (), and equilibrium quantity () into the elasticity formula.
Equilibrium
EquilibriumThe price elasticity of supply at equilibrium is .
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