If Individual A's demand was Q=10-2P, Individual B's demand was P=10-2Q, and market supply was P=Q, what is the market equilibrium is the subsidy is 8 dollars?
To find the market equilibrium with a subsidy, we first need to understand how the subsidy affects supply and demand.
Usually, a subsidy given to consumers means that for each unit a consumer buys, they effectively pay less than the market price by the amount of the subsidy. This type of subsidy shifts the demand curve to the right. On the other hand, a subsidy given to producers lowers their costs by the subsidy amount, effectively allowing them to sell at a lower price while still covering their costs, which shifts the supply curve to the right.
Let's assume the subsidy is given to consumers and adjust Individual A's demand to reflect that.
Original Individual A's demand: \( Q = 10 - 2P \)
With the $8 subsidy, Individual A effectively pays $8 less for each unit, so we adjust the price downwards by $8 when they purchase:
Adjusted Individual A's demand: \( Q = 10 - 2(P - 8) = 10 - 2P + 16 = 26 - 2P \)
We should adjust Individual B's demand similarly using the subsidy:
Original Individual B's demand: \( P = 10 - 2Q \)
After subsidy, Individual B is willing to pay $8 more at each quantity level because they're being subsidized:
Adjusted Individual B's demand: \( P + 8 = 10 - 2Q \)
\( P = 2 - 2Q \)
Now, to find the market demand, we need to sum up Individual A and B's demand:
Market Demand = Individual A's Demand + Individual B's Demand
\( Q_A + Q_B = (26 - 2P) + (2 - 2P) \)
\( Q_A + Q_B = 26 + 2 - 2P - 2P \)
\( Q_A + Q_B = 28 - 4P \)
Now, let's set the market demand equal to the market supply (which doesn't change due to the subsidy):
Supply: \( P = Q \)
So:
\( 28 - 4P = P \)
Solving for P:
\( 28 = 5P \)
\( P = \frac{28}{5} \)
\( P = 5.6 \)
With the market price at $5.6, we find the equilibrium quantity by plugging the price back into the supply equation since the firm's supply decision isn't affected by the subsidy received by the consumer:
\( Q = P \)
\( Q = 5.6 \)
At a market price of $5.6, the equilibrium quantity is 5.6 units.
However, please note that Individual B's original demand function written as \( P = 10 - 2Q \) does not need to be adjusted for a consumer subsidy since it is already expressed in terms of the price they are willing to pay; therefore, Individual B's demand stays the same. Moreover, if the subsidy is not a consumer subsidy but a producer subsidy or if it affects the market in a different manner, the equilibrium calculation would change accordingly. This solution assumes a consumer subsidy that reduces the effective price faced by the consumer. Please clarify if the subsidy applies in a different manner or if there are additional conditions.