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pm 74% Tue 11:45 PM a E Safari File Edit View History Bookmarks Window Help 6 F 400 M E smartsite.ucdavis.edu McAfee a Secure Search k 2600 Chegg Study I Guided Solutions and... Pandora Radio Listen to Free Intern... SmartSite@UCDavis ARE 100B A01-A https://smartsite.ucdavis.edu/access Chegg.com eS 9. Suppose a firm faces the inverse demand curve P 100 Q. Marginal cost is constant at $10. me a. Calculate producer surplus and the deadweight loss under monopoly pricing. b. Suppose the firm uses block pricing, selling the first 45 units at $55 per unit, the next 20 pe 2 units at $35 per unit, and the next 20 units at $15 per unit. Calculate producer surplus and the dead weight loss under block pricing. DVoo WSers Contro e Pics Work

Solution

1)

To find the profit maximizing quantity and price we first need the MR curve for the monopolist.

MR = 100 – 2Q

Then, set MR = MC to solve for Q:

100 – 2Q = 10 or Q = 45

When Q = 45, then P = 100 – Q = 100 – 45 or P = $55

Total Revenue = ($55 per unit)(45 units) = $2475

Total Cost = ($10 per unit)(45 units) = $450

Profits = TR – TC = $2475 - $450 = $2025

Consumer Surplus = (1/2)($100 per unit - $55 per unit)(45 units) = $1012.50

Producer Surplus = ($55 per unit - $10 per unit)(45 units) = $2025

Dead Weight Loss = (1/2)($55 per unit - $10 per unit)(90 units – 45 units) = $1012.50

2) Now first 45 at $55 and next 20 at $35 and $15 respectively

So 1/2(55-10*45) + 1/2(35-10*20) + 1/2(15-10*20)

= 1312.50

Dead-weight loss

(1/2)($55 per unit - $10 per unit)(90 units – 45 units) = $1012.50