Question

5. Public Goods Three individuals consume a public good, and their demands are expressed as:

P1 = 1.5 - 0.005Q (for Q < 300);

P2 = 4.5 - 0.007Q (for Q < 643);

P3 = 3.0 - 0.002Q (for Q < 1500),

where P represents price in dollars per unit and Q represents output in units per day. The marginal cost of providing the service is given as a constant $5.00 per unit. Determine the efficient level of output of this public good.

Answer 1

For finding the efficeint level of output of public good , we sum the prices of the individuals and compare it to MC .

when in private good , we equate the prices individually to the marginal cost and not their sum.

so here in public good adding the individual prices , we get

P1+P2+P3 = 1.5 - 0.005Q+4.5 - 0.007Q + 3.0 - 0.002Q

since we need to aggregate them , its important to have an interval which is common for all 3 of them . so the interval which is common is from 0 to 300 (0<Q<300) , since all 3 equations satisfy this .

adding up we get

\P= 9-0.014Q

so Q= 4/0.014 = 285. 7 or 286

this would be the optimum level of the public good which is also less than 300.

if it would have been more than 300 then only P2 and P3 would have been there.