(Scenario: Freedonian Exports) In the small country of Freedonia, the domestic demand for widgets is represented by P = 100 - 3Q; the domestic supply of widgets is represented by P = 1Q. What is the value of total subsidy payments to Freedonia's widget exporters?
A) $825
B) $600
C) $225
D) $125

Question

Quizplus · Accepted Answer

To find the value of total subsidy payments, we need to first find the equilibrium quantity and price without any subsidy. Setting the demand and supply equations equal to each other, we get:
100 - 3Q = Q
4Q = 100
Q = 25
Substituting Q = 25 in either the demand or supply equation, we get the equilibrium price:
P = 100 - 3(25) = $25
Now, let's assume that the government provides a subsidy of S per unit of widget exported. This means that the effective price for the exporter would be P + S. The exporter would supply where their marginal cost equals the effective price, which is simply the supply equation:
P + S = Q
25 + S = Q
Therefore, the quantity of widgets exported with the subsidy is also 25. However, the effective price is now P + S = $25 + S. This price must be equal to the price received by the exporter in the absence of a subsidy, which is $1. Therefore,
$25 + S = $1
S = -$24
This negative value for S means that the government is providing a subsidy of $24 per unit of widget sold. Since the quantity exported is 25, the total subsidy payment would be:
Total subsidy payments = 25 x $24 = $600

(Scenario: Freedonian Exports) in the Small Country of Freedonia, the Domestic