The inverse demand for soda is P = 25 - 0.2Q. The supply for soda is P = 6 + 0.8
ID: 1189450 • Letter: T
Question
The inverse demand for soda is P = 25 - 0.2Q. The supply for soda is P = 6 + 0.8Q, where P is in thousands of dollars and Q is in thousands of sodas. The market for soda is perfectly competitive.
The equilibrium quantity in the market is 19 thousand sodas.
The equilibrium price in the market is 21.2 thousand.
The government wants to encourage alternative sources of energy and decides to offer soda producers a subsidy of $2 thousand per soda produced and sold. As a result, the new equilibrium quantity in the market will be ___ thousand sodas. The amount sellers will receive for each soda sold is $ ___ thousand. The amound buyers will pay for each turbine purchased is $___ thousand. The deadweight loss caused by the subsidy is $___ million. (Round answers to one decimal place).
Explanation / Answer
QD =Quantity demanded, PB =Price for buyer
QS =Quantity supplied, PS =Price for seller
NQS= New quantity demanded
Q= Equilibrium quantity
P= Equilibrium price
PB = 25 - 0.2QD or 0.2QD = 25 –PB
Thus, QD = 25/0.2 – 1/0.2P = 125 – 5PB
Similarly, PS = 6 + 0.8QS or QS= 1.25P – 7.5
Now after a subsidy of 2 New PS = PS + 2
Thus, NQS = 1.25(PS +2) – 7.5 = 1.25PS – 5
In equilibrium, QD = NQS and PB=PS=P
Thus, 125P – 5P = 1.25P -5
6.25P =130 or P=130/6.25 = 20.8
New Q= 1.25 (20.8) -5= 26 -5 =21
Hence total quantity = 21
PB= 20.8
NPS= 20.8 +2= 22.8
Dead weight loss is the area of the triangle, with the base =2 (size of subsidy) and height= New - Old equilibrium quantity= 21-19 =2
Hence, deadweight loss = ½ *2*2= 2
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