Answer to Question #264315 in Microeconomics for Nara

Question

1. Demand for grain is given by function Qd=9-4P and supply - by function Qs=2P. The government also entered the market and bought 6 units of the grain. Which equilibrium price will be established in this market and how much grain will be sold?

2. Price elasticity of demand and income elasticity of demand are accordingly -0,4 and 1,1. The changes in price and income accordingly amounted to 12% and -5%. Find the percentage change in quantity demanded.

3. Price elasticity of demand, last sale, last price, and initial price accordingly are -1,5; 20; 10; 40. Find the initial sale.

Answer 1

Solution:

1.). At equilibrium: Qd = Qs

9 – 4P = 2P

9 = 2P + 4P

9 = 6P

P = 1.5

Equilibrium price = 1.5

Substitute to derive equilibrium quantity:

Qd = 9 – 4P = 9 – 4(1.5) = 9 – 6 = 3

Equilibrium quantity = 3

New equilibrium quantity = 3 + 6 = 9

 

2.). Price elasticity of demand = % change in qty demanded/ % change in price

-0.4 = % change in qty demanded/12%

% Change in qty demanded = -0.4 x 12% = -4.8%

 

Income elasticity of demand = % change in qty demanded/ % change in income

1.1 = % change in qty demanded/-5%

% Change in qty demanded = 1.1 x -5% = -5.5%

 

3.). Price elasticity of demand = % change in qty demanded/ % change in price

Initial sale = 11