EC2B3 problem set 7
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London School of Economics**We aren't endorsed by this school
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ECONOMICS EC2B3
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Economics
Date
Dec 20, 2024
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2
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1 EC2B3 Macroeconomics II Problem Set 7 Lent Term 2023 1.Stabilizing business-cycle fluctuations using monetary policy: Consider the New Keynesian model with completely sticky goods prices. Assume wages are flexible and adjust so demand equals supply in the labour market, which implies the real wage is equal to households’marginal rate of substitution between leisure and consumption (? = ???𝑙,𝐶). Assume all households are alike with consumption demands depending negatively on real interest rate ?. In equilibrium, households are savers. Firms must borrow to finance investment at interest rate ?𝑙, so investment is determined by ?𝑃𝐾′− 𝑑 = ?𝑙, where ?𝑃𝐾′− 𝑑is the future marginal product of capital net of depreciation. There is a spread ? = ?𝑙− ?between the interest rate ?𝑙paid by borrowers and the interest rate ?received by savers. Suppose a financial crisis leads lenders to expect more defaults in the future. This results in a higher interest-rate spread ?. (a)What is the effect of a higher interest-rate spread ?on the output demand curve ?𝑑? Assuming the stance of monetary policy remains unchanged (a horizontal ??line with a constant nominal and real interest rate ?0), what happens to real GDP ?and employment ?? Suppose the central bank adjusts monetary policy to close the gap between actual GDP and the ‘natural level of output’(GDP if prices were fully flexible) after the shock to ?. (b)Show in a diagram what adjustment of the real interest rate ?is required for this. After the increase in ?and the monetary policy response, what are the overall effects on ?, ?𝑙, consumption ?, and investment 𝐼? (c)Explain why the monetary policy change in part (b) benefits households in terms of getting closer to a level of employment where ?𝑃𝑁= ???𝑙,𝐶. 2.Short question: Consider the model with strategic complementarity across employment at different firms coming from positive spillover effects on productivity. Show using diagrams that the economy can have multiple levels of GDP consistent with market clearing if the spillovers are strong enough to make the aggregate labour demand curve upward sloping and steeper than the labour supply curve.
2 3.For discussion: What factors might affect whether monetary or fiscal policy is a more effective tool in stabilizing an economy hit by demand shocks? 4.The financial accelerator and macroprudential policy: Capital is purchased either by investors who can make a profit of ?per unit of capital, but whose own financial resources limit how much capital they can purchase, or by deep-pocketed investors who face no such limits, but who can only make a profit ? < ?on the marginal unit of capital they purchase (because they are less skilled in putting capital to use). The first group’s capital purchases 𝐾are subject to the budget constraint 𝑉𝐾 = ? + 𝐸and the binding collateral constraint ? = 𝑉′𝐾/(1 + ?), where 𝑉is the price of capital, 𝑉′is the future capital price, ?is borrowing, 𝐸is the net worth or equity of this group, and ?is the real interest rate. Since the collateral constraint is binding, the second group of investors is the marginal purchaser of capital and the capital price is 𝑉 =𝑉′1 + ?+?(𝐾)1 + ?where ?(𝐾)is the second group’s marginal product, an increasing function of 𝐾(the more capital the first group holds, the less need for the second group to buy capital). (a)Show that ?(𝐾)𝐾 = (1 + ?)𝐸and deduce that the first group’s capital purchases 𝐾are positively related to their equity 𝐸. Hence explain why higher equity 𝐸causes ?(𝐾)and the price of capital 𝑉to rise. Initial equity is 𝐸 = (?? + 𝑉)𝐾̃− (1 + ?)?̃, where 𝐾̃and ?̃are past capital purchases and borrowing, and ?is the fraction of profits that can be retained to build up equity. Given past capital, debt, and interest rates, higher capital prices 𝑉boost equity 𝐸. (b)Explain why the model features a ‘financial accelerator’, a positive feedback loop between the price of capital 𝑉and equity 𝐸of the most effective group of investors. The financial accelerator magnifies the effects of a shock to equity 𝐸on investment. To avoid this amplifying business-cycle fluctuations, suppose regulators use macroprudential policy to limit borrowing to ? = (1 − 𝑚)𝑉′𝐾/(1 + ?)with 𝑚 < 1. (c)Find the leverage ratio 𝑉𝐾/𝐸in a steady state where 𝐸′= 𝐸and 𝑉 = 𝑉′. (d)With reference to your answer to (c) and the elasticity 𝑉𝐸𝜕𝐸𝜕𝑉of equity with respect to the capital price, explain intuitively why macroprudential policy can reduce the strength of the financial accelerator.