Question

Функции спроса и предложения для некоторого товара имеют вид Qd=70-0.4p, Qs=-50+2p. Определить:a) Условие рыночного равновесия (равновесную цену и равновесный объем);b) Величину расходов правительства, необходимых для поддержания равновесия на рынке при фиксированной цене 80 руб.

Answer 1

Решение:

Qd=Qs

70-0,4p=-50+2p

2,4p=120 

p=50 - равновесная цена

Qd=70-0,4*50 = 50

Qs= -50+2*50 = 50

Qd=Qs=50 - равновесное количество

При фиксированной цене товара 80 руб.

Объем спроса составит:

Qd=70-0,4*80 = 38 (величина расходов правительства, необходимых для поддержания равновесия на рынке)

Объем предложения составит:

Qs= -50+2*80 = 110

Итак, объем предложения будет выше объема спроса. Образуется излишек товара в размере:
QS - QD =  110 - 38 = 72.

 

Answer 2

Market Equilibrium Condition

To determine the market equilibrium condition, we need to find the price and quantity at which the quantity demanded (Qd) equals the quantity supplied (Qs).

The demand function is given as: Qd = 70 - 0.4p [[1]]. The supply function is given as: Qs = -50 + 2p [[2]].

To find the equilibrium price, we set Qd equal to Qs and solve for p: 70 - 0.4p = -50 + 2p

Simplifying the equation: 2p + 0.4p = 70 + 50 2.4p = 120 p = 120 / 2.4 p = 50

The equilibrium price is 50 rubles.

To find the equilibrium quantity, we substitute the equilibrium price (p) into either the demand or supply function. Let's use the demand function: Qd = 70 - 0.4p Qd = 70 - 0.4 * 50 Qd = 70 - 20 Qd = 50

The equilibrium quantity is 50 units.

Therefore, the market equilibrium condition is a price of 50 rubles and a quantity of 50 units.

Government Expenditure to Maintain Market Equilibrium

To maintain market equilibrium at a fixed price of 80 rubles, the government needs to intervene by adjusting the quantity supplied or demanded. In this case, the government would need to increase the quantity supplied to match the quantity demanded at the fixed price.

To determine the government expenditure required, we need to find the difference between the quantity demanded and the quantity supplied at the fixed price.

Substituting the fixed price (p = 80) into the demand and supply functions: Qd = 70 - 0.4p Qd = 70 - 0.4 * 80 Qd = 70 - 32 Qd = 38

Qs = -50 + 2p Qs = -50 + 2 * 80 Qs = -50 + 160 Qs = 110

At the fixed price of 80 rubles, the quantity demanded (Qd) is 38 units and the quantity supplied (Qs) is 110 units. The difference between the quantity demanded and supplied is 110 - 38 = 72 units.

Therefore, the government would need to intervene by supplying an additional 72 units of the product to maintain market equilibrium at the fixed price of 80 rubles. The government expenditure required would depend on the cost of producing and supplying these additional units.