Time Allowance: You have 2 hours to complete this examination, plus additional collation time of 20 minutes and an Upload Window of 20 minutes.  The additional collation time has been provided to cover any additional tasks that may be required when collating documents for upload, and the Upload Window is for uploading, completing the Cover Sheet and correcting any minor mistakes. The additional collation time and Upload Window time allowance should not be used for additional writing time.

If you have been granted SoRA extra time and/or rest breaks, your individual examination duration and additional collation time will be extended pro-rata and you will also have the 20- minute Upload Window added to your individual duration.

All work must be submitted anonymously in a PDF file and you should follow the instructions for submitting an online examination in the AssessmentUCL Guidance for Students.

If you miss the submission deadline by up to 40 minutes late in the Late Submission Period, a late submission penalty will be applied unless you submit a valid claim for Technical Failures. At the end of the 40-minute Late Submission Period, you will not be able to submit your work via AssessmentUCL and you will not be permitted to submit the work via email or any other channel.  If you are unable to submit your work or have submitted your work late during the Late Submission Period due to technical difficulties which are substantial and beyond your control, you should submit a claim for Technical Failures via the AssessmentUCL Query Form. For detailed information on the regulations relating to online assessments conducted on the AssessmentUCL digital platform, please refer to Section  10 of the Student Regulations for Exams and Assessments 2022-23.

Query  on  the  Examination  Paper:  If you  have  a  query  about  the  examination paper, instructions or rubric, you should complete an AssessmentUCL Query Form. Please note that you will not receive a response during your examination.

Academic Misconduct: By submitting this assessment, you are confirming that you have not violated UCL’s Assessment Regulations relating to Academic Misconduct contained in Section 9 of Chapter 6 of the Academic Manual.

QUESTIONS

Answer any 5 questionsfrom Section A and all questionsfrom Section B.

Questions in Part A carry 10 per cent of the total mark each, questions in Part B carry 25 per cent of the total mark each (5 per centfor each sub-question).

PART A

Answer any 5 questions from this section.

1.   A country is described by the Solow model with no population growth with a production           function in terms of income per capita of y = k  . Suppose that k is equal to 400. The fraction   of output invested is 50%. The depreciation rate is 5%. Is the country at its steady-state level of output per worker, above the steady-state, or below the steady state? Show how you reached     your conclusion.

2.   Suppose that in a particular country, GDP per capita was $1,000 in a given year and $8,000 36 years later. Using the rule of 72 approximate the annual growth rate of GDP per capita. Has     any real-world country achieved a growth rate close to this over 3-4 decades in the past?

3.   Consider a balanced growth path of a neoclassical economy with labor-augmenting                  technological progress and a constant returns to scale Cobb-Douglas production function, as in the Solow and Romer models. The growth rate of technology A and capital K is 2% per           annum. The growth rate of population is 0% per annum. What is the growth rate of                  consumption per capita?

a.   0%

b.   2%

c.   Cannot say based on information given.

4. People in a society have the utility function U = log c + ψlogR where c is consumption and R is the environmental quality. Show mathematically that the utility function is concave in both      arguments. Plot the marginal utility of consumption and of environmental quality on two             separate graphs. Then, assuming that c = Y/L  = E! L"!  and R = R(−1) − E , where R (−1) is  the starting level of environmental quality, calculate the formula for the optimal energy intensity E/Y . What happens to it over time? How would your answer change if there was technological

progress that meant that output was increasing over time?

5. Give two examples for the reasons why we might see a permanent (or at least a very long-     lasting) increase in the saving rate in an economy (in particular, think of two reasons why there could be an exogenous shift upwards in the saving rate in the Solow model).

6. Consider a Romer model with population growth n=0% and an interest rate r=5%. Assume that patents are granted for the duration of only 2 years. What is the price (or value) of a patent that   grants exclusive rights to sell a newly invented product when the sales of this product bring        $1million of profits annually? You can do your calculations either in discrete or in continuous    time.

7. Do you expect the private value you calculated in the previous question to be above, equal to, or below the social value from having the product available in the market over these two years? Explain your answer briefly (you do not need to do any calculations, but you might want to use a simple diagram with a downward sloping demand curve for the product).

8. Are these two statements true or false?

a.   Business stealing effect, as highlighted by the Schumpeterian model of growth, suggests that there may be too much effort / resources spent on innovation in    equilibrium, relative to what is best for society.

b.   In practice, the evidence generally tends to suggest this is indeed the case and the governments should therefore tax R&D.

9. Consider a model of international technology diffusion / imitation. The frontier of technology (OECD, say) is characterized by a balanced growth path in the Romer model, with population  growth of 1% per annum. Assume that parameter  , which denotes the diminishing returns to

knowledge accumulation in the OECD, is 0. A developing country is growing at 2% per annum. Is this developing country on a balanced growth path? Explain your answer.

10.  There are two firms in the economy, with technologies Y#  = L#  and Y2  = 6L2 , where L#  and    L2  are the labor inputs of the two firms, respectively. Labor is paid marginal product in each firm. There is L units of labor in the economy. Calculate how much labor each firm employs. Then       assess the degree of misallocation in this economy.

PART B

Answer all questions from this section.

B1          Using the Solow model we studied in class (the variant with no population growth or

technological change), trace out the effect of an increase in the saving rate on a country’s capital per worker and income per capita.

a.   Show how to derive the formula for the steady state capital to output ratio. How does it depend on the saving rate?

b.   Show how to derive the formula for the steady state income per capita. How does it depend on the saving rate?

c.   Show how to derive the formula for the steady state consumption per capita. How does it depend on the saving rate?

d.   Starting from an initial steady state, trace out graphically the trajectory (using the Solow diagram) following an increase in the saving rate.

e.   Plot output per capita and consumption per capita over time, starting before the time when the saving rate jumped.