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1. a. Consider the following production function: Q = K⅔L⅓. Explain the specialcharacteristics of this production function. How is it different from a Linear production function? How is it different from a Leontief production function?(8 marks)
b. Assuming that the firm hires 10 units of capital and 20 units of labour, use the production function given in part a to compute the average and marginal products of labour. (8 marks)
c. Explain how the firm would use the marginal product of labour to determine the profit maximizing quantity of labour which the firm would hire.(4 marks)
2. A firm produces the following units of output, Q, by hiring a fixed quantity of capital, K, and labour, L, as follows:
L: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
Q: 16, 36, 65, 97, 137, 177, 209. 233, 249, 257
a. Determine the average and marginal products of labour. (6 marks)
a. Provide rough graphs of the total product, average product and marginal product curves and explain why they behave in the way they do. Be sure to label your axes correctly. (4 marks)
c. Assuming that the cost of capital is $1,000 and labour costs $10.00 per hour, determine the total variable cost, average variable cost and the marginal cost of the firm for the output levels given above.
d. Provide rough graphs of the TVC, AVC and MC curves and compare their behaviour with the product curves in part b. Be sure to label your axes correctly. (4 marks)
3. Assume that a firm hires only labour and capital to produce bicycles
a. Explain the cost minimization rule for this firm and why this rule is logical…(8 marks)
b. Suppose that the firm hires 100 units of capital and 500 units of labour and that the MPl is 20 while MPk is 25. If a unit of labour costs $4.00 and a unit of capital costs $5.00, is the firm minimizing costs? Explain.