Economics help pls.... cost of subsidy?

Question

demand equation : Q = 36 - 4P

supply equation : Q = -6+2P

the government subsidizes producers of the commodity at the rate of $3/unit.

Find cost of subsidy.

Answer 1

forget all the fancy formulas which matter not in a free economy.

the cost of subsidy is

the total amount of subsidy

divided by the number of taxpayers who are getting screwed

plus the costs of creating and administering the subsidy

Answer 2

I am sure you know the standard textbook answer.  Since the producer gets subsidy for each unit ouput produced, his marginal cost gets reduced by $3 for each marginal unit. This means that the marginal cost curve just shifts down lower by this amount. Since the Marginal cost curve (when it starts rising), is the supply curve of the firm. So the supply curve shifts parallely down by $3 meaning that the producers willing to supply the same quantiti now at price P-3 as they were supplying at price P. So the supply equation now gets changed to as follows: first transpose the original as 2P= Q--6 0r, .P= Q/2 - 3, now reduce the value od P by the amount of subsidy so that P= Q/2 - 6 , 0r, 2P= Q-12 0r,Q= -12 +2P

Now, we get the equilibrium output by equating demand and supply: 36-4(P*)= Q*= - 12+ 2P*, where * denotes the equilibrium values. Thus, 36-4P*= -6+2P*-6, 0r, 48= 6P*, which means P*= 8 :at P=8, demand Q*= 36- 4*8= 4.

The cost of subsidy therefore is $3*4= $12. It is surprising that with subsidy, the output goes down from the orginal equilibrium output. Check

Why not give the subsidy to the consumer?

There are different ways of looking at the problem as a layman economics student.Since it is not mentioned whether the demand equation is post subsidy or not, there are two possibilities: The demand equation already incorporates the subsidy of $3 per unit realised as additional revenue by the producers. Or, it is not.

Case A: If it is the first case, we just for demand supply equlibrium with 36-4P*=Q*=-6+2P* where 8 denotes equlibrium values of P and Q, So, 6P*=42 0r, P*= 7 and using that in any of the equations we get Q*= 36-4*7=36-28=8 or

Q*= -6 +2*7= -6+14= 8 .

sINCE the rate SUBSIDY, is $3/unit the cost of subsidy is

$3*Q*= $388= $24

Case B;  With the subsidy, the demand curve shifts parralley upwards to the right by $3 implying the demand eqaution becomes (P+3)= 36/4 - Q/4 or 4P + 12 = 36 - Q or, Q= 24-4P

now we solve for demand supply equality as before.

24-4P*= Q*= -6 +2P8, or, 6P*=30 or, P*=5 and then get the equlibrium output as Q*= 36- 4*5= 16 . So the producers will produce double the output than before subsidy was introduced and make a sales revenue of P* Q*= $5*16= $80 plus a subsidy income of $3*16= $48. So the subsidy cost is $48.

Most likely Case B is your question.