Question

Consider a mine. A new earthmover costs $2,000,000. The depreciation rate is 10%. The real interest...

  1. Consider a mine. A new earthmover costs $2,000,000. The depreciation rate is 10%. The real interest rate is 6%

    1. (a) What is the value of the earthmover after 1 year?

    2. (b) What is the marginal cost of a earthmover?

      The additional earthmover allows the mine to transport an additional 300 tonnes of raw materials/week. Each ton is valued at $20.

    3. (c) What is the Marginal Product of Capital (MPK)?

    4. (d) What is the Marginal Revenue Product of Capital (MRPK)?

    5. (e) Is it optimal for the firm to own the earthmover?

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Answer #1

a)

Cost of earthmover=P=$2,000,000

Depreciation=d=6%

Depreciation in year 1=D1=P*d=2000000*10%=$200,000

Value of earthmover after 1 year=P-D1=2000000-200000=$1,800,000

b)

Marginal Cost is the sum of depreciation and interest lost during the year of operation in this case,

Interest lost in year 1=I1=2000000*6%=$120,000

Marginal Cost in year 1=D1+I1=200000+120000=$320,000

c)

Marginal Product of capital=MPK=300 tons per week* 52 weeks=15600 tons

d)

Marginal Revenue Product of capital=MRPK=MPK*Price=15600*20=$312,000

e)

We observe that MRPK is higher than the marginal cost. So, it is optimal to use earthmover.

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