Answer to Question #264141 in Microeconomics for Mim

Question

Andrew, Beth and Cathy live in Lindhville. Andrew’s demand for bike paths, a public good, is given by Q=12-P. Beth’s demand is Q=18-P and Cathy’s is Q=8-(P/3) The marginal cost of building (a kilo-meter of path) is MC=$21.

(a)      Find the socially desirable (Pareto Efficient) amount of bike paths (in kilo-meters).

(b)      What is the total cost of building the amount bike paths you found in (a).

(c)      How would government charge the individuals to cover its costs (i.e., how much each individual be charged for a unit bike path and how much each of them will end up paying in total.

Answer 1

Find the inverse demand functions as Andrew’s demand $Q=12-P$, Beth’s demand $Q=18-P$ and Cathy’s demand $Q=24-3P$.

Market demand for public good is $Q=12-P+18-P+24-3P$

or $Q=54-5P$ .

The marginal cost MC = $21.

A - Socially desirable amount of bike paths is

$Q=M\times C$

$54-(5\times P)=21$

$P=\frac{33}{5}=6.6$ km

B - Total cost of building the amount bike paths = 6.6 x 21 = 138.6.

C - Andrew will pay $Q=12-6.6=5.4$ for each kilo-meter, Beth will pay $18-6.6=11.4$ for each kilo-meter and Cathy will pay $24-(3\times6.6)=4.2$ for each kilo-meter.

In total Andrew will pay $5.4\times6.6=35.64$ Beth will pay $11.4\times6.6=75.64$ and Cathy will pay $6.6\times4.2=27.72$.