a monopolist, has a total cost curve given by TC = 5Q + 15. He sets two prices for his product, a regular price, PH, and a discount price, PD. Everyone is eligible to purchase the product at PH. To be eligible to buy at PD, it is necessary to present a copy of the latest Vietnam Electrics newspaper ad to the salesclerk. Suppose the only buyers who present the ad are those who would not have been willing to buy the product at PH.

demand curve is given by P = 20 – 5Q, what are the profit-maximizing values of PH and PD?

To find the profit-maximizing values of PH and PD, we need to analyze the monopolist's pricing strategy based on the given information. Here's how we can approach it step by step:

1. Determine the monopolist's profit-maximizing output level (Q):
To maximize profit, the monopolist should produce the quantity at which marginal cost equals marginal revenue. In this case, the marginal revenue is equal to the regular price (PH) since the discount price only applies to those who present the newspaper ad.

Given that the demand curve is P = 20 – 5Q, we can solve for Q when marginal revenue (MR) equals marginal cost (MC). To find MR, take the derivative of the demand curve with respect to Q:

MR = d(P)/d(Q) = 20 - 10Q

Set MR equal to MC, which is the derivative of the total cost function TC = 5Q + 15:

20 - 10Q = 5

Solving this equation, we find Q = 1.

2. Determine the regular price (PH):
To find PH, substitute the value of Q into the demand curve equation:

P = 20 - 5Q
P = 20 - 5(1)
P = 20 - 5
P = 15

The regular price (PH) is therefore 15.

3. Determine the discount price (PD):
Based on the given information, only those who would not have been willing to buy the product at the regular price (PH) present the newspaper ad to be eligible for the discount price (PD).

Since everyone else is eligible to purchase at PH, it means that the demand at PH (Q=1) equals zero. So, we need to find the price level where Q=0.

Setting Q = 0 in the demand curve equation:
0 = 20 - 5Q
0 = 20 - 5(0)
0 = 20

Since there are no buyers at Q=0, the discount price (PD) doesn't matter because no one is willing to pay for the product at this price. Therefore, the monopolist does not need to set a discount price (PD) in this scenario.

Therefore, the profit-maximizing values are:
PH = 15
PD = None (No discount price needed)

The monopolist sets the regular price at 15, and there is no discount price as the demand at the regular price satisfies all potential buyers.