An investor invests 70% of her wealth in a risky asset with an expected rate of return of 15% and a variance of 0.05 and she put
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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 :
and the supply equation will be:
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,
P = $6.2093
Substituting the value of P in the demand equation, we get,
units
b. Calculation of Price Elasticity of supply at equilibrium level.
P₀ = $4
Q₀ = 61
P₁ = $6.2093
Q₁ = 67.7442
% change in quantity = 11.05607%
% change in price = 55.2325%
Price Elasticity of Supply (PES):
PES = 11.05607% / 55.2325%
PES = 0.20
