ECO2003F - Anele is a Farmer in the Cape Winelands - Economics Assignment Help

Assignment Task

Question 1 – Production
Anele is a farmer in the Cape Winelands, and produces wine using labour and machinery.
Anele produces wine according to the production function.
a. Draw a representative isoquant for Anele, making sure to label your graph carefully. What relationship holds between machinery and labourers in Anele’s production process?
b. Assume that Anele currently employs 3 labourers, and owns 4 pieces of machinery. Calculate the marginal products of labour and machinery in her production process. 
c. What is the marginal rate of technical substitution for Anele, assuming that she still employs 3 units of labour and 4 pieces of machinery?
d. What is the optimal ratio of machinery to labour that Anele should employ in her production process? If Anele still hires 3 labourers, how many machines should she use?

Question 2 – Production
Thato owns a small artisan coffee shop where he produces his own coffee. The process of producing coffee requires him to roast beans before grinding them, and this production process requires him to hire workers and ovens.

a. Carefully describe the difference between the concepts of “diminishing marginal returns” and “decreasing returns to scale”. Which of these characteristics does Thato’s production function exhibit? Make sure to explain your answer clearly.
b. Derive an expression for Thato’s average product of labour.
c. Derive an expression for Thato’s marginal product of labour and his marginal product of ovens.
d. If Thato currently uses 16 ovens and 4 workers, use your answers from 2.2 and 2.3 to determine whether average product of labour would increase or decrease by hiring a 5th worker. Include a diagram in your explanation.
e. Determine a general expression for Thato’s marginal rate of technical substitution (MRTS). What does this suggest about the relationship between capital and labour? Hint: Consider how the MRTS changes as we increase K or L.
f. What is Thato’s MRTS when he employs 16 ovens and 4 workers? How would you interpret this value?

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