{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

econ11_08_ps8

# econ11_08_ps8 - Eco11 Fall 2008 Simon Board Economics 11...

This preview shows pages 1–2. Sign up to view the full content.

Eco11, Fall 2008 Simon Board Economics 11: Practice Problems 8 (Weeks 9–10) December 3, 2008 1. First Welfare Theorem There are two goods ( x and y ) and two agents (A and B). The agents’ utility functions are u A = v A ( x ) + y u B = v B ( x ) + y where v A = 2ln( x ) and v B ( x ) = 4 x 1 / 2 , The agents have incomes m A = 10 and m B = 10. The price of good y is p y = 1; the price of good x is to be determined. A single ﬁrm produces good x . It has cost function c ( q ) = q 2 / 2. (a) Show that p = 2 is an equilibrium price. Find the equilibrium allocations ( x A ,x B ,q ). (b) Suppose a social planner chooses ( x A ,x B ,q ) to maximise the total surplus, v A ( x A ) + v B ( x B ) - c ( q ) subject to q = x A + x B . Verify your allocations from part (a) satisfy the FOCs from this optimisation problem. 2. Shifts in Supply Functions Suppose the supply function is q = p , and the demand function is q = 10 - p . (a) Find the equilibrium price and quantity.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

econ11_08_ps8 - Eco11 Fall 2008 Simon Board Economics 11...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online