Answer:
$2 per-unit subsidy.
Explanation:
So, we are given the following data or parameters or information in the question above;
=> "The inverse demand for the product is P = 24 - q. "
=> "Jon's cost function is C(q)=q^{2}. "
(1). For profit to be maximized the value of Margin Revenue, MR = marginal cost, MC.
MR = marginal cost= dTR/ dq, where TR = p × q = (24 - q ) q = 24q - q^2.
MR = marginal cost = 24 - 2q.
Also, marginal cost, MC = dCq/dq = d/dq × (q)^2.
marginal cost, MC = 2q.
MR = MC; 24 - 2q = 2q.
q = 6.
NB: Pm = 24 - qm.
Pm = 24 - 6 = $18.
(2). For optimum quantity; p = marginal cost.
24 - q = 2q.
q* = 8.
p* = 2 × 8 =$ 16.
On a price versus quantity curve, the dead weight loss = area shaded under the curve.
Quantity to produce = 12.
At MC* = MR, Qm = Q* and On= p*.
The amount of per-unit subsidy be to completely eliminate the deadweight loss = 18 - 16 = $2.
