08.05.2023 Tutorial 1#

1)#

Best Repsonse Curve

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  • higher childcare subsidys for working people:

    • more effort

    • reservation wage decreases (cost of job loss higher)

    • \(\gets\) BRC

      • lower reservation wage and higher effort!

  • higher demnd for firms output

    • No Effect on Reservation Wage!

    • no Effect on BRC

  • improved technology

    • effort \(\uparrow\), no effect on reservation wage

    • BRC rotates (to left)

=> RBC only moves with Reservation Wage or effort!

Reality: workers only Effort, but never lesser wage! (sticky wages)

2#

Profit of Firm $\( \Pi = \underbrace{p \cdot f(zeH)}_{revenue} - \underbrace{wH}_{cost} \)$

  • H = hours per week

  • z = Technology

  • e = effort

  • w = wage

  • p = price

  • f() = production function

Effort Function: $\( e = E(w) = \Big(\frac{w-v}{v}\Big)^a \)$

  • v = outside option (e.g unemployment benefits)

  • a = degree of substitution

Diff w.r.t. \(w\) $\( \begin{aligned} \frac{\delta \Pi}{\delta w} &= p \cdot f'(zE(w)H) * zE'(w)H- 1H = 0 \\ &= \bigg[p f'\big(zE(w)H\big)*zE'(w)-1\bigg]H = 0 \\ &= p f'(zE(w)H)*zE'(w) = 1 \end{aligned} \)$

3)#

Decrease in Unemployment Benefit

  • higher effort for every wage

  • BRC to left

Monitoring Device

  • increasing effort at given wage

  • detection of shriking more likely

  • BRC upwards

Decrease in Disutility of Working

  • more effort at every wage