Riemann surface
matlab

Question 1: Short questions
(a) Suppose that, in a closed economy, the central bank adjusts the money supply in such a manner that the interest rate, $R$, is constant. Derive the slope of the AD curve. Show what happens to the LM curve as a result of the central bank’s policy.
(b) What do we mean with the notion that capital and labour are cooperative production factors? Can you give an example where this holds true?
(c) Assume that firm investment depends only weakly on the interest rate. Does that make the IS curve very steep or relatively flat? (In the usual diagram with the interest rate on the vertical axis and real output on the horizontal axis.)
(d) What are the two most important differences between the views of the classical and Keynesian economists?
(e) Consider the usual diagram with the real wage on the vertical axis and employment on the horizontal axis. Perfectly competitive firms use capital and labour to produce output. Why must competitive labour demand functions be downward sloping? Why must capital and labour be cooperative factors of production?

Question 5: Tax incidence
In the book we have developed a very simple model of the aggregate labour market. Suppose that we write this model as follows:
$$\begin{array}{rlrl} N^D & =N^D(W / P, \bar{K}), & & N_{W / P}^D=\frac{1}{F_N N}<0, \quad N_{\bar{R}}^D=-\frac{F_N K}{F_N N}>0, \ W / P & =g\left(N^S\right), & & g_N>0, \ {\left[N \equiv N^D\right.} & =N^S, & \end{array}$$
where $N^D$ is labour demand, $W$ is the nominal wage, $P$ is the price level, $\bar{K}$ is the capital stock, $N^S$ is labour supply, and $N$ is equilibrium employment. We assume that the expected price is equal to the actual price $\left(P^e=P\right)$ and that the labour market is in equilibrium. Answer the following questions about this model. Use graphical means as much as possible.
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EXERCISE \& SOLUTIONS MANUAL
(a) What do we assume implicitly in equation (Q1.11) about the income and substitution effects in labour supply? Explain intuitively how these effects operate.
(b) Assume that the government introduces a so-called payroll tax ( $\left.t_W\right)$, i.e. a tax levied on employers which is proportional to the firm’s wage bill. The payroll $\operatorname{tax}$ is thus a tax on the use of labour by firms. This tax changes the definition of profit for the representative firm to: $\Pi \equiv P F(N, \bar{K})-W\left(1+t_W\right) N$. Explain the effect of the payroll tax on the demand for labour.
(c) Demonstrate the effects of an increase of the payroll tax on employment $(N)$ and the gross real wage $(W / P)$. Who ends up ultimately paying the payroll tax-the firms or the worker-households?
(d) Introduce a value-added (consumption) tax $\left(t_C\right)$ in the simple labour market model. Explain what happens to employment $(N)$ and the gross real wage $(W / P)$. Who ultimately pays the tax?
(e) Use the insights from questions (b)-(d) to analyse the effects of a costly improvement of labour conditions. Who pays the costs eventually and who benefits from the improvements?

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