Assume that the government decides to subsidise the suppliers of solar panel with a specific subsidy equal to 40. Prior to the subsidy the supply curve for solar panels is given by the following: p = 50 +3Q. The demand for solar panels is given by the following: p = 450 – Q. Which of the following statements is true.

Question

BlackTom AI · Accepted Answer

The problem involves a per-unit subsidy to solar panel suppliers and asks for the total cost of the subsidy, given the pre-subsidy supply and demand, and the subsidy amount.
First, note the pre-subsidy supply is p = 50 + 3Q and the demand is p = 450 − Q.
With a subsidy s = 40 paid to suppliers, the price received by producers is higher than the price paid by consumers by s. That is, p_producer = p_consumer + s.
So we can write the equilibrium condition as: p_producer = 50 + 3Q = p_consumer + s = (450 − Q) + 40.
Simplifying: 50 + 3Q = 490 − Q ⇒ 4Q = 440 ⇒ Q = 110.
Next, the price paid by consumers is p_consumer = 450 − Q = 450 − 110 = 340. The price received by producers is p_producer = p_consumer + s = 340 + 40 = 380. These values are consistent with the shifted supply and original demand.
Now, the total cost of the subsidy to the government equals the subsidy per unit times the quantity subsidized: Total subsidy cost = s × Q = 40 × 110 = 4400.
Evaluating the options:
- The total cost of the subsidy is 40. This would be only the per-unit subsidy, not the aggregate cost, so it’s incorrect.
- The total cost of the subsidy is 1100. This does not match the calculated 4400, so it’s incorrect.
- The total cost of the subsidy is 4000. This is close but not equal to the computed 4400, so it’s incorrect.
- The total cost of the subsidy is 4400. This matches the calculation s × Q = 40 × 110 = 4400, so it is the correct total subsidy cost.
- None of the above. Since 4400 is a valid calculation, this option is incorrect.

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