Question 1

Peter and Jane are utility-maximisers and they have both an income of 20 pound, which must be allocated between beer (good 1) and pizza (good 2). It is known that the price of a bottle of beer is 2 pound and the price of a pizza is 6 pound. Peter has diminishing marginal rate of substitution for the two goods. His
marginal rate of substitution is: . Jane’s utility function is instead:
π‘ˆ(π‘žπ΅, π‘žπ‘ƒ) = π‘šπ‘–π‘›{π‘žπ΅, 2π‘žπ‘ƒ}. For each consumer, answer the following questions:

(i) Calculate the optimal quantity of beer and pizza and show it in a diagram. (20 marks)
(ii) Now suppose that the price of beer decreases to 1 pound. Calculate the impact of the fall in the price of beer on the optimal demand of the two goods, show the effect in a diagram and comment.
(10 marks)
(iii) Show the substitution and income effects in a diagram and comment.
(10 marks)
(iv) On the basis of your analysis, draw the demand curve for beer and
the effect of the fall in the price of beer on the demand for pizzas.
(10 marks)

Question 2

Firms A and B both use capital and (unskilled) labour as factors of production. Firm A has a Cobb-Douglas production function: π‘ž = 𝐾𝛼𝐿𝛽. This implies the marginal rate of (technical) substitution is: . Let us assume that 𝛼 =
0.8 and 𝛽 = 0.2. Firm B has instead the following technology: π‘ž = 6𝐾 + 4𝐿. Wages are equal to 10,000 Β£ and the cost of capital is also equal to 10,000 Β£.

For each firm, answer the following questions:

(i) Calculate the optimal quantity of capital and labour, show the solution in a diagram and comment. (20 marks)
(ii) Derive the total cost function, draw it in a diagram and comment on the shape. (10 marks)
(iii) Now suppose that the price of capital increases to 15,000 Β£. Calculate the impact of the increase in the price of capital on the optimal demand for capital and labour, show the effect in a diagram and comment.
(15 marks)
(iv) Show how the total cost function changes following the increase in the price of capital. (5 marks)

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