Public economics question (1 Viewer)

[elkedag]

There's no answers that I can find and I don't actually understand what I'm doing, but any ideas about this one?

A lone shepherd can graze 10 sheep per year in a meadow. Each additional shepherd who uses the meadow reduces the number of sheep that can be maintained by one per shepherd. If a person would rather stay home than graze fewer than four sheep:

- How many shepherds will lead their flocks to the meadow every year?
- What is the efficient number of shepherds at the meadow?

I'm having trouble figuring out SMB for the efficient number, and the answers I'm getting don't make sense.
Any help would be much appreciated!! Thanks

 

[Orwell]

Do you have the actual answers with you? What were the answers you were getting?

 

[elkedag]

There's no actual answers, but I think that SMB is n(11-n) [or 11-2n??], and SMC = 4 where n is the number of shepherds, so I get answers like 3.5 which doesn't seem right. But I'm really confused about SMB in this question.

 

[Orwell]

I got 7 for the first one and 5 for the second one.....I'm more than likely wrong. Sorry </3

 

[elkedag]

What did you get as the SMB and MC for the efficient quantity question?

I'm thinking SMB = 11 - 2n because n = 5.5 maximises the number of sheep, so its derivative is zero? But I really have no idea

 

[Orwell]

I have no idea what those terms mean. I simply took an 'opportunity cost' approach. I only have a year 11 eco knowledge basis but thought I'd give it a go. I drew it out.

 

[elkedag]

SMB is social marginal benefit and MC is marginal cost if that helps.
And I'm assuming that the meadow is some sort of impure public good and everyone derives utility from the provision of sheep, because it's under the 'public goods' chapter

 

[Amundies]

What did you get as the SMB and MC for the efficient quantity question?

I'm thinking SMB = 11 - 2n because n = 5.5 maximises the number of sheep, so its derivative is zero? But I really have no idea

It's been a while since I've done economics, so this is more maths related. If SMB = 11 - 2n, then the derivative is never 0. It's just a straight line, I think you might be thinking that it's a curve (a sad face curve, presumably)?

 

[elkedag]

It's been a while since I've done economics, so this is more maths related. If SMB = 11 - 2n, then the derivative is never 0. It's just a straight line, I think you might be thinking that it's a curve (a sad face curve, presumably)?

I meant the derivative of 'total benefit' which is n(11-n).
But to be honest, I have no idea what to take as SMB here.

 

[Amundies]

Ah ok, that would make sense then.

 

[elkedag]

Any other ideas on how to do this question (especially the efficiency part - there's another part which requires you to calculate net social benefits, so SMB is needed for that too)?

This is question 12 from chapter 4 of the Rosen and Gayer textbook (Public Finance) by the way