Question

Given a demand curve of P=105-1.25 Q and a supply curve of P=5+1.25 Q , with a subsidy of 10, solve for the resulting quantity.

Answer 1

To solve for the resulting quantity, set the demand and supply equations equal to each other and solve for Q. The resulting quantity is 40 units and the price is $55.

Step-by-step explanation:

To solve for the resulting quantity, we need to set the demand and supply equations equal to each other:

105 - 1.25Q = 5 + 1.25Q

Subtracting 1.25Q and 5 from both sides yields:

100 = 2.5Q

Dividing both sides by 2.5, we get: Q = 40

So, the resulting quantity is 40 units.

Solving for the price can be done by substituting the quantity value into either the demand or supply equation:

P = 105 - 1.25(40)

P = 105 - 50

P = 55

Therefore, with the subsidy of 10, the resulting quantity is 55. The subsidy shifts the effective supply curve upward by the subsidy amount, leading to a lower equilibrium quantity and a higher equilibrium price. In this case, the subsidy reduces the quantity exchanged in the market from the equilibrium quantity in the absence of the subsidy.