1. (10 marks) Consider an economy that only produces 2 goods: apple and banana. Unit prices and quantities (in tons) produced in 2 years are given by the following table:

Compute Real GDP in year 2 under the Chain-weighted approach, using year 1 as the reference year. Show full working. Use 3 decimal places.

2. (10 marks) Consider the model of the household and firm studied in class. Suppose that there is a temporary increase in total factor productivity z. What are the effects on labour supply, labour demand and wage rate in equilibrium? Use diagram to support your answer.

3. (10 marks) Suppose that you are interested in isolating the cyclical component of a macroeconomic time series (such as GDP, consumption…).

a) (5 marks) Why assuming a non-linear trend would be preferable than assuming a linear trend?

b) (5 marks) With regards to business cycle regularities, is consumption more or less volatile than GDP? Explain.

4. (10 marks) Consider the model of the household and the government studied in class. The government decreases current taxes, while holding government spending in the current and future period constant. What are the effects of this fiscal policy on consumption? (Hint: Think about the effect of this policy on lifetime wealth of consumers.)

PART B: PROBLEM SOLVING QUESTIONS

ANSWER ALL QUESTIONS. MARKS ARE AS INDICATED (TOTAL: 60 MARKS)

Note: Show full working and use 3 decimal places for calculation questions.

1. (35 marks) Consider the Two-Period Endowment Model of household behaviour studied in class. The household derives utility from consumption today ��� and consumption tomorrow ���′. Suppose that preferences are represented by the utility function:

���(���, ���^′) = ���^��� + ���(���^′)^���

where ���, ��� ���(0, 1)

The household receives exogenous income ��� today and ���′ tomorrow. For simplicity, assume that there are no lump-sum taxes (i.e. ��� = ���^′ = 0, using the notation in class). The real interest rate is given by ���.

a) (5 marks) Write down the problem of the household.

b) (10 marks) Solve for the optimal level of current consumption (i.e. ���^∗).

c) (5 marks) Suppose that the parameters of the model take the following values:

��� = 500, ���^′ = 105, ��� = 0.95, ��� = 0.08, ��� = 0.3.

Based on these values, is the household a lender or a borrower? Justify your answer.

d) (5 marks) Suppose that now the interest rate ��� decreases to 0.05 (while the values ofall other parameters are unchanged). Compute the new level of optimal consumption in the first period. What does your finding imply about the relative magnitudes of income and substitution effects? Explain.

e) (10 marks) Using a diagram on the (���, ���^′) plane, illustrate  the  effect of a decrease in ��� on the optimal consumption bundle of the household who is a lender, and identify income and substitution effects. Would the consumer be better-off or worse-off after the decrease in the interest rate?

Note: To answer Part (e), you don’t need to do any algebra or calculations.

2. (25 marks) Consider the model of the representative firm studied in class. Recall that in this model, the firm lives for two periods, producing output ��� in the first period, and output Y’ in the second period by operating the following technologies:

��� = ������(���, ���^���), ��������� ���^′ = ���^′���(���^′)

where (���, ���^′) denotes physical capital in the first (second) period, ���^��� is labour demanded in the first period, and ���, ���^′ denotes total factor productivity in the first (second) period. The function ��� is increasing in both arguments, it is concave, and it satisfies constant returns to scale. The function ��� is increasing and concave.

The firm hires labour in a competitive market at the wage ���. Capital in the first period ��� is fixed, and physical capital depreciates at the rate ��� ∈ (0, 1) between periods, so that: ���^′ = (1 − ���)��� + ���, where ��� denotes investment.

The firm discounts future payoffs using the interest rate ���, and the objective of the firm is to maximise the present value of its profits.

a) (5 marks) Suppose that thanks to modern technology, the capital depreciation rate decreases. What would be the effect on the firm’s investment decision?

b) (5 marks) Suppose that the government introduces a wage subsidy in the amount ��� > 0 per unit of labour demanded by the firm. Write down the firm’s problem.

c) (7 marks) What are the effects of this subsidy to labour demand? Draw diagram that illustrate your answer.

d) (8 marks) Assuming that there is no subsidy and ��� = ���^′ = 1, ��� = 0.02, ��� = 0.05, ��� = ���^0.3���^0.7, ��� = (���′)^0.5, ��� = 40

Compute the optimal level of investment of the firm ���^∗.