Question

The government wants to help the mohair sweater industry by giving producers a specific subsidy of ​$1.20 per mohair sweater. Suppose that the market demand isgiven​ by: Upper Q Superscript d Baseline equals 1200 minus 22 p and the market supply​ is: Upper Q Superscript s Baseline equals negative 220 plus 40 p. How much will the subsidy cost​ taxpayers?

Answer 1

$855.79

I got it right on the test

Answer 2

$855.79

Step-by-step explanation:

`Q^(d)` = 1,200 - 22p .................................... (1)

`Q^(s)` = - 220 + 40p .................................... (2)

When a subsidy of $1.20 is given, it will increase the price of the producers by $1.20 and Qs becomes:

`Q^(s)` = -220 + 40(p + 1.2) = - 220 + 40p + 48

`Q^(s)` = -172 + 40p .............................................. (3)

At equilibrium,
`Q^(d)` =
`Q^(s)`. Equating equations (1) and (3) and solve for equilibrium price p, we have:

1,200 - 22p = -172 + 40p

-22p - 40p = -172 - 1,200

-62p = -1,372

p = -1372/-62

p = 22.129

Substitute p into equation (3) to obtain equilibrium quantity, Q, we have:

`Q^(s)` = -172 + 40(22.129) = -172 + 885.16 = 713.6

Cost of subsidy to taxpayers =
`Q^(s)` * Subsidy per unit = 713.6 * 1.2 = $855.79