1 | Pageof 1Assignment #2: Intermediate Microeconomic Theory IDue: February 27th, 2013Note: This...

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1 | Pageof 1Assignment #2: Intermediate Microeconomic Theory IDue: February 27th, 2013Note: This assignment is composed of three questions. You are encouraged to work in groups; however, you must formulate and write your own solutions. You must also show all your work.Question #1Suppose the production function for guitars is given by: q = LK– .4L2where q is the number of guitars manufactured per week L is the number of person-hours per weekK is the number of machine-hours per week.i)If K = 50, derive the total product function and draw it over the range of L = 0 to L = XXXXXXXXXXmarks) Sketch the marginal product and the average product curves. (4 marks) At what level of L does the average product reach its maximum? (4 marks) At what level of L does the marginal product reach its maximum? (2 marks)ii)Duplicate your analysis in part i) using K = XXXXXXXXXXmarks with same marking scheme as i)) iii)When K = 50 or when K =75, does the total product curve have a region of increasing marginal returns? (5 marks) Does it have a region of diminishing returns? (5 marks)Question #2Suppose that a firm uses both labour (L) and capital (K) as inputs and has the long run production function q = LK – L, with MPL = K – 1 and MPK = L. Capital rents for $150 and labour can be hired for $75 per day. i)Suppose that we are in the short-run and capital is fixed at K = 4. What is the production function? (6 marks)If the firm wishes to produce q = 30, what combination of inputs should it use to produce as efficiently as possible? (5 marks)ii)Calculate the MRTS when L = 3 and K=30? (6 marks) Briefly explain the meaning of MRTS for this production function. (6 marks)iii)What is elasticity of substitution when the capital-labour ratio changes from 110 to 130? (10 marks)Question #3Suppose a firm uses both labour (L) and capital (K) as inputs and has the production function q = 2KL. The marginal product of labour is 2K. The marginal production of capital is 2L. If capital rents for $200 and labour can be hired for $100 per day and the firm is minimizing costs:i)What is the total cost of producing q units of output? (5 marks) What is the average cost of producing q units of output? (5 marks) What is the marginal cost of producing q units of output? (5 marks)ii)What combination of capital and labour should it use to produce q = 64? (12 marks) What would be the cost of production? (6 marks)

005_zk-pxaojivv.pdf

Robert · Accepted Answer

Q1
i.
q= 50L -.4L2
	L
	Q
	AP
	MP
	0
	0
	 
	 
	5
	240
	48
	48
	10
	460
	46
	44
	15
	660
	44
	40
	20
	840
	42
	36
	25
	1000
	40
	32
	30
	1140
	38
	28
	35
	1260
	36
	24
	40
	1360
	34
	20
	45
	1440
	32
	16
	50
	1500
	30
	12
	55
	1540
	28
	8
	60
	1560
	26
	4
	65
	1560
	24
	0
	70
	1540
	22
	-4
	75
	1500
	20
	-8
AP= q/L= 50 -.4L
This is maximum when L= 0
MP = dq/dL = 50-.8L
This is also maximum when L= 0
ii.
q= 75L -.4L2
AP= q/L= 75 -.4L
This is maximum when L= 0
MP = dq/dL = 75-.

1 | Pageof 1Assignment #2: Intermediate Microeconomic Theory IDue: February 27th, 2013Note: This assignment is composed of three questions. You are encouraged to work in groups; however, you must...

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