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EC210

Macroeconomic Principles

Section A

(Answer both questions below.)

Question 1

Consider two economies, A and B. Both have the same population and all figures given below are per person for each economy. Economy A has GDP $100,000 and B has GDP £150,000. The market exchange rate between the currencies used in A and B is $1 = £2. Both economies produce a man- ufactured good and services (which include childcare). Manufacturing is 25% of the value of market output in both economies. The market price of a manufactured good is $1,000 in Economy A and £2,000 in Economy B. Services have price $100 in A and £100 in B.

The capital stock (made up of manufactured goods) in Economy A is $100,000 and £100,000 in Econ- omy B. Capital depreciates at rate 10% in both economies. Economy A has net foreign income of −$10,000 and Economy B has net foreign income of £20,000.  In Economy B, all childcare is pro- vided within the family, whereas in Economy A, all childcare is purchased in the market. Including non-market work, people in Economy B work the same number of hours as people in Economy A.

Assuming all else is equal, in which economy do you think people are better off? Give a careful justi- fication of your answer.                                                                                      [20 marks]

Question 2

Consider a model of human capital accumulation. Goods are produced using only human capital according to the production function Y = zuH, where H denotes the economy’s supply of human capital, u is the fraction of human capital allocated to producing goods, and z is the exogenous and fixed level of total factor productivity. Assume the population is constant over time, so H is propor- tional to average human capital per person, and output per person is proportional to Y.

A fraction 1 − u of current human capital is allocated to producing future human capital, which is determined by the equation H′ = M + b(1 − u)H, with M > 0 being the minimum amount of human capital if all workers were unskilled, and b > 1 giving the productivity of the production process for human capital.

By plotting H′ − H against H in a diagram, derive a condition for u such that there exists a steady state for human capital H and no long-run growth in Y. Explain why there is always some value of u > 0 such that this model generates positive long-run growth in H and Y.

In the case where the model generates long-run growth in Y, if each worker receives a wage equal to z multiplied by their human capital, explain what must happen over time to the ‘skill premium’, the ratio of the wages of high-skilled to unskilled workers.                                              [20 marks]

Section B

(Answer the one question below.)

Question 3

Consider the Solow model. An economy produces aggregate output Y using capital K and labour N. The production function is Y = zKα N1一α , where z is total factor productivity and α is a parameter that lies between 0 and 1. Next year’s capital stock K′ is given by K′  = I + (1 − d)K, where I is investment and d is the rate at which capital depreciates over time. There is no population growth (n = 0), so N′  = N, and TFP z is constant over time. Investment is equal to saving sY, which is a

constant fraction s of income.                                                                             [60 marks]

(a)    Derive an expression for the per-worker production function y = zf (k), where y = Y/N and

k = K/N are output and capital per worker. Solve for the steady-state capital per worker k*

and output per worker y* that satisfy the equation sy = dk.                               [10 marks]

Suppose the country had reached its steady-state level of capital per worker and is now hit by severe flooding that destroys a part of its capital stock. Assume this is treated as a one-off event that is not expected to reoccur.

(b)    Using a diagram showing y, sy, and dk, explain what happens to income per worker in the short

run, in the long run, and in the transitional period between the two.                        [6 marks]

Now suppose that owing to climate change, flooding will occur more frequently than before. Treat this as an increase in the capital depreciation rate d.

(c)    Using the diagram from part (b), illustrate the long-run effect of higher d on capital per worker k and income per worker y.                                                                           [8 marks]

(d)    Assume that α = 1/3 and d = 0.1 initially. If, for example, climate change raised d from 10% to 11%, what is the approximate long-run effect on y as a percentage of its initial level? [Hint: Derive an equation for log y*, where y* is the steady-state value of y from part (a), and recall that the percentage change in a variable x is approximately the change in log x.]               [10 marks]

(e)    If α = 1, meaning that the production function becomes Y = zK, an ‘AK’ production function,

explain how the effects of higher d are qualitatively different from what you found in part (c).

[8 marks]

The Golden rule level of capital accumulation gives the highest sustainable level of consumption per worker c = (1 − s)y, sustainable in the sense that y must be equal to the steady-state value implied by the saving rate s.

(f)    Show how to derive a first-order condition for the Golden rule capital stock per worker kG(*)R  in

terms of the marginal product of capital ∂Y/∂K = zf′ (k), and find the effect on kG(*)R following

the climate-change induced rise in d.                                                                 [8 marks]

(g)    Does the saving rate sGR  needed to get to the Golden rule kG(*)R  rise, remain the same, or fall

when climate change increases d?                                                                   [10 marks]