g Jon owns a company in Santa Barbara that has a patent on a specialized product. The inverse demand for the product is P = 24 - q. Jon's cost function is C(q)=q^{2}. Concerned about the high price that Jon charges for his product, the government decides to subsidize Jon so as to eliminate the deadweight loss. How much must the per-unit subsidy be to completely eliminate the deadweight loss?

$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.