{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

review1_sol

# To have the optimal level of labor input n w,r,y = y

This preview shows pages 4–7. Sign up to view the full content.

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

View Full Document

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.

Unformatted text preview: to have the optimal level of labor input: N ( W,R,Y ) = Y AN φ T ! 1 β + γ βR γW γ β + γ Notice that the optimal K is proportional to the optimal N , K ( W,R,Y ) = γW βR N ( W,R,Y ) = Y AN φ T ! 1 β + γ γW βR β β + γ b) The cost function is given by: C ( W,R,Y ) = WN ( W,R,Y ) + RK ( W,R,Y ) = Y AN φ T ! 1 β + γ " W βR γW γ β + γ + R γW βR β β + γ # = ( Y ) 1 β + γ ( A )- 1 β + γ ( N T )- φ β + γ " W βR γW γ β + γ + R γW βR β β + γ # c) The derivative of the cost function with respect to A and N T are: ∂C ∂A =- 1 β + γ ( Y ) 1 β + γ ( A ) 1 β + γ- 1 ( N T )- φ β + γ " W βR γW γ β + γ + R γW βR β β + γ # < ∂C ∂N T =- φ β + γ ( Y ) 1 β + γ ( A )- 1 β + γ ( N T ) φ β + γ- 1 " W βR γW γ β + γ + R γW βR β β + γ # < d) No. If more productive firms disproportionately locate in NYC, the average cost can be lower in NYC without higher agglomeration externalities. 3. Private Provision of Public Goods: (a) Suppose Falco contributes C F for the concerts and Mozart contributes C M . Then, the total amount of concerts enjoyed by Falco and Mozart are C M + C F . Falco’s maximization problem is: max X F ,C F U = ln X F + ln( C M + C F ) subject to 70 = X F + C F The Lagrange function associated with this problem is: L = log X F + log( C M + C F )- λ ( X F + C F- 70) Taking derivatives and setting them equal to zero, yields: ∂ L ∂X F = 1 X F- λ = 0 ∂ L ∂C F = 1 C M + C F- λ = 0 Eliminating the Lagrange multiplier yields: X = C M + C F Substituting this optimality condition into the budget constraint yields: 70 = 2 C F + C M which yields the following reaction function: C F = 70- C M 2 Since Falco and Mozart have identical preferences and income, we get for Mozart the following reaction function: C M = 70- C F 2 Substituting Mozart’s reaction function into Falco’s yields: C F = C M = 70 / 3 = 23 . 334 Hence there would be 46.667 concerts. (Each individual would also enjoy 46 . 667 units of the private good.) (b) With the government intervention, Falco’s maximization problem changes to: max X F ,C F U = log X + log( C M + C F + 10) subject to 65 = X F + C F Setting up the Lagrange function and computing the first order conditions yields: ∂ L ∂X...
View Full Document

{[ snackBarMessage ]}

### Page4 / 11

to have the optimal level of labor input N W,R,Y = Y AN φ...

This preview shows document pages 4 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online