Question

Suppose that Barton’s demand for fireworks (which for now we assume to be a private good) is QB = 25 − 5P and Jay’s demand is QJ = 10 − 2P.

What is the social marginal benefit of firework consumption? That is, what is the willingness of society to pay for fireworks? (society in this problem and in b means Barton + Jay, and this question boils down to horizontal summation of quantities demanded vs vertical summation of prices or willingness to pay). Write down your answer as P being a function of Q (e.g., Jay’s willingness to pay for fireworks is P = 5 − QJ /2, which is just his individual demand function, inverted to be in terms of Q rather than P).

Answer 1

The social marginal benefit of firework consumption is found by horizontally summing Barton's and Jay's demand functions, resulting in the combined demand function QS = 35 - 7P. Inverted, this becomes P = 5 - Q/7, representing society's willingness to pay for fireworks.

Step-by-step explanation:

The social marginal benefit of firework consumption is the willingness of society to pay for an additional unit of fireworks. To find this, we horizontally sum Barton's and Jay's individual demand functions.

Barton's demand for fireworks is given by QB = 25 − 5P, and Jay's demand is QJ = 10 − 2P. To determine the combined demand, we add the quantities at each price, which results in QS = QB + QJ.

By substituting the individual demand equations into the combined demand, we get QS = (25 − 5P) + (10 − 2P) = 35 − 7P. Inverting this equation to solve for P as a function of Q, we find P = 5 − QS/7. This represents the price (willingness to pay) associated with each quantity Q of fireworks demanded by society.