Question

The government wants to help the mohair sweater industry by giving producers a specific subsidy of ​$1.10 per mohair sweater. Suppose that the market demand isgiven​ by: Upper Q Superscript d Baseline equals 1100 minus 20 p and the market supply​ is: Upper Q Superscript s Baseline equals negative 230 plus 40 p. How much will the subsidy cost​ taxpayers? The cost to taxpayers is ​$ nothing ​(Round your answer to the nearest​ penny.)

Answer 1

$12.47

Step-by-step explanation:

Given;

Demand = Qd = 1100 - 20p .......................................... (1)

Market supply = Qs = - 230 + 40p ..............................(2)

The subsidy of $1.10 by the govern will increase the price of the producers by $1.10 and Qs in equation (2) becomes:

Qs = - 230 + 40(p + 1.10)

Qs = - 230 + 40p + 44

Qs = -186 + 40p ....................................................................(3)

At equilibrium, Qd = Qs. Equating equations (1) and (3) and solve for equilibrium price p, we have:

110 - 20p = -186 + 40p

110 + 186 = 40p + 20p

296 = 60p

p = 296 / 60

p = 4.93

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

Qs = -186 + 40(4.93) = 11.33

Cost of subsidy to taxpayers = Qs * Subsidy per unit = 11.33 * 1.10 = $12.47.