Question

Roberta runs a dress factory. She needs to produces 80 dresses per day, using a combination of labor and sewing machine. She can hire as much labor as she wants at a cost of $10 per unit. She can rent as much sewing machine as she wants at a cost of $2.5 per unit. Her production function is y=5L^1/2M^1/2, where L is the amount of labor and M is the amount of machine.

a. Write the equation for MRTS is: MRTS=

M/L

2M/L

M1/2/L1/2

M/2L

(Hint: MPL=2.5L^-1/2M^1/2, MPM=2.5L^1/2M^-1/2

b. Find out Roberta’s demand for L and M, which can produce 100 dresses in the cheapest possible way. She needs M=Answer and L=Answer (please enter integer numbers)

c. Based on the solution from question b, calculate the lowest cost to product 100 dresses. The lowest cost=$Answer (please enter an integer)

d. The local government raised the minimum wage from $10 to $22.5 per unit, ie the cost of labor is $22.5 now. With the new prices, calculate the lowest cost to produce 60 dresses. The lowest cost=$Answer (please enter an integer)

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