ECO-5007B:– Assessment 1


This assessment is worth 30% of the module mark. Answer ALL four questions. The TOTAL number of marks available for this assessment is 50 MARKS.

You need to submit one answer document to the module Blackboard site by 15:00 (UK time) on Thursday 24th March.


Question 1 [10 marks]

Investigate whether the assumption that the government can borrow more cheaply than private households (i.e., 𝑟𝐺 < 𝑟) can lead to a violation of Ricardian Equivalence. (Your answer is likely to benefit from being supported by an appropriate diagram.)


Question 2 [15 marks]

Mary lives for two periods. In the first period she gets a real wage 𝑌1 of £5,000, and in the second period a real wage 𝑌2 of £6,000. She knows with certainty what her second-period wage will be and obeys her intertemporal borrowing constraint.


  • Mary chooses to consume £5,400 in period 1 and £5,540 in period 2. Find the real interest rate, 𝑟. Draw Mary’s intertemporal budget constraint, making sure that you show

the slope and both intercepts of the constraint.                                                   [3 marks]


  • Assume that the real interest rate changes to 10% and that Mary still consumes £5,540 in period 2. Graphically, numerically, and verbally discuss the effects of the interest rate

change on Mary’s consumption in both periods.                                                 [6 marks]


  • Instead assume that Mary’s wages remain unchanged (i.e., 𝑌1 = £5,000, 𝑌2 = £6,000) and that the real interest rate is 10%, but Mary also receives an inheritance of £500 at the start of period 1 and will leave £500 to future generations (i.e., will have £500 left at the end of period 2). What is the maximum Mary could consume in period 1 (i.e., 𝐶1𝑀𝐴𝑋)?

[3 marks]


  • George obeys his intertemporal budget constraint and lives for three periods with real income as summarised in the table below. George can borrow and save at the real interest rate that is 10%.
Period Real income (£)
1 5,000
2 5,500
3 6,000


i. What is the maximum George can consume in period 1?   [1 mark]
ii. What is the maximum George can consume in period 2?   [1 mark]
iii. What is the maximum George can consume in period 3?   [1 mark]


Question 3 [20 marks]

Economy 1 can be described by the following production function, where output 𝑌 is produced with physical capital 𝐾, human capital 𝐻, and labour 𝐿,

𝑌 = 𝐹(𝐾, 𝐻, 𝐿) = 𝐾𝛼𝐻𝛽𝐿1−𝛼−𝛽

Here, labour 𝐿 grows at rate 𝑛, but there is no technological progress.

(a) Show that this production function exhibits constant returns to scale.   [2 marks]


(b) What is the per-worker production function, 𝑦 = 𝑓(𝑘, ℎ)?   [2 marks]

In Economy 1, households save a fraction 𝑠𝐾 of their income in physical capital and a fraction 𝑠𝐻 of their income in human capital and that 𝑠𝐾 = 𝑠𝐻 = 𝑠. Both forms of capital depreciate at the rate 𝛿. Physical and human capital accumulation are given by,

∆𝑘 = 𝑠𝑓(𝑘, ℎ) − (𝛿 + 𝑛)𝑘  ∆ℎ = 𝑠𝑓(𝑘, ℎ) − (𝛿 + 𝑛)ℎ

  • Find an expression for the steady-state level of output per worker (in terms of 𝑠, 𝑛, 𝛿, 𝛼, and 𝛽). [6 marks]


  • What is the growth rate of output in the steady state? Explain your answer. [2 marks]


Now consider Economy 2, with both technological progress and population growth, described by the production function,


𝑌 = 𝐹(𝐾, 𝐴𝐿) = 𝐾0.3(𝐴𝐿)0.7


Here 𝑌 is output, 𝐾 is capital, 𝐿 is labour, and 𝐴 is a measure of technological progress. Further, assume that 𝐴 grows at rate 𝑎, 𝐿 grows at rate 𝑛, and that capital depreciates at a rate of 4%. The economy starts in a steady state with constant output per effective worker. In this steady state, output 𝑌 grows at a rate of 6% and the capital-output ratio (𝐾⁄𝑌) is 4.


  • What is the saving rate for Economy 2?                                                            [2 marks]


  • Suppose that the saving rate changes such that Economy 2 transitions to the GoldenRule steady state. What is the capital-output ratio at the Golden-Rule steady state? What is the new saving rate?                                                                                [4 marks]


  • Draw a diagram with time, 𝑡, on the horizontal axis, and consumption on the vertical axis to show how consumption increases and/or decreases as Economy 2 transitions from the starting steady state to the Golden-Rule steady state. Was this economy initially in a dynamically efficient or dynamically inefficient steady state? Explain your answer.

[2 marks]

Question 4 [5 marks]

Suppose the Bank of England decides to start selling its holdings of longer-maturity government debt. (This is the opposite of quantitative easing, sometimes called quantitative tightening.) Explain what effect such a policy might have on long-term bond yields? Is there a limit to the credibility of this policy approach for affecting long-term yields?






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