Determine equilibrium quantity

Question

Following equations denote market for widgets
Demand: P = 10 - Q Supply: P = Q - 4

Here P mentions the price in dollars per unit and Q mention the quantity in thousands of units. Assume the government has a change of heart regarding the importance of widgets to the happiness of the American public. The tax is eliminated and a subsidy of $1 per unit is granted to widget producers. Determine equilibrium quantity be? What price will the buyer pay? What amount per unit (by including the subsidy) will the seller attain? What will be the net cost to the government?
The original supply curve for widgets was P = Q - 4. Along with a subsidy of $1.00 to widget producers, the supply curve for widgets shifts outward. Remember that the supply curve for firm is its marginal cost curve. Along with a subsidy, the marginal cost curve shifts down by the amount of the subsidy. The new supply function is following:
                                                                           P = Q - 5.
To obtain the new equilibrium quantity, set the new supply curve equal to the demand curve:
                                                                           Q - 5 = 10 - Q, or Q = 7.5.
The buyer pays P = $2.50, and the seller attain that price plus the subsidy, that means, $3.50. Along with quantity of 7,500 and a subsidy of $1.00, the net cost of the subsidy to the government will be $7,500.