Recall the regulation model where legislators apply regulations to garner votes. Votes are a function of producer utility (UR ) and consumer utility (UC ). The legislator’s vote/utility function is V = V(UR , UC ). If U R = R, and U C = K – R – L, where K is a constant and R and L are the typical monopoly versus competitive market outcome below. Obviously, both U R and U C are affected by the eventual price (P) set by the legislator because both R and L are affected by that price. (a) Now suppose the demand equation is given by P = 100 - Q , and MC = $20. Write R as a function of the price and show that the price that maximizes producer utility is $60. (b) Given the MC and demand equation above, find the maximum possible consumer surplus (hint: this will be when the market is competitive). (c) Now suppose that (in addition to the information in parts d and e), the legislator gets votes according to V (U R, U C ) = 3U R + U C . Find the price that maximizes the legislator’s votes.
1. Recall the regulation model where legislators apply regulations to garner votes. Votes are a function of producer utility (UR ) and consumer utility (UC ). The legislator’s vote/utility function is V = V(UR , UC ). If U R = R, and U C = K – R – L, where K is a constant and R and L are the typical
Obviously, both U R and U C are affected by the eventual
(a) Now suppose the demand equation is given by P = 100 - Q , and MC = $20. Write R as a function of the price and show that the price that maximizes producer utility is $60.
(b) Given the MC and demand equation above, find the maximum possible
(c) Now suppose that (in addition to the information in parts d and e), the legislator gets votes according to V (U R, U C ) = 3U R + U C . Find the price that maximizes the legislator’s votes.
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