Question 1

Mr Phill owns a farm that produces maize, his cost of production can be represented by the

following cost function: 4000Q - 1600Q2 + 200Q3

. Where Q is the quantity of maize

produces in tons.

a) Find the level of output at which ATC is minimized (6)

b) How much TC, ATC, and MC will Mr Phill incur to produce at a cost minimizing

output? (6)

c) Given a Mr Phill's current level of capital and labour inputs, the marginal product of

labour for his production is 3 units of output. If the marginal rate of technical

substitution between capital and labour is 9, what is the marginal product of capital?

Show your work. (4)

Question 2

A manufacturing firm has a production function where its marginal rate of technical

substitution is - K/L, the cost of labour is N$100, the cost of capital is N$50 and the total cost

of production is N$500 000

a) Write the isocost equation of the firm and draw a well labelled isocost curve with

labour on the horizontal axis and capital on the vertical axis, indicating the capital and

labour intercepts (8)

b) Calculate the slope of the isocost line? (2)

c) What are the quantities of labour and capital representing the optimal resource

allocation for the firm? (6)

d) Show the optimal resource allocation in c) on a fully labelled graph, with capital on

the vertical axis. (5)

Question 3

Mr Edward's farm employs two factors of input (labour and capital) to produce and its aim is

to maximize profit.

a) Assume that Mr Edward is not employing a cost-minimizing combination of labour

and capital, the MPL is 9 and the MPK is 3, wage rate is N$3 and the rental rate of

capital is N$0.50. In your opinion, do you think it is sensible for Mr Edward to hire

more labour and less of capital? Elaborate your answer. (5)

b) Explain the meaning of the cost-minimization rule. (3)

c) What will happen if he hires more labour and less capital? Elaborate in details. (5)

Question 4

Hector Octagon makes t-shits. Their t-shirts are identical to the ones other manufacturers are

making. Hector Octagon's daily cost information is as follows: TC = 100 + 20Q + 2Q

2

, the

current market price for t-shirts is N$ 100 per t-shirt

a) How many t-shirts should Hector Octagon make to maximize their profit in a short

run? Show your work. (5)

b) How much profit will they make?