Question #60436

a) Given TC = 30 + 3q + 4q^2 + q^3, determine the values for AFC, AVC, ATC, and MC at
Q = 5.
b) Graphically illustrate and describe the relationship between the cost curves in
part (a).
c) Derive and explain the relationship between marginal cost and marginal product. Describe the law of diminishing marginal returns and how it relates to marginal cost and marginal product.

Expert's answer

a) TC = 30 + 3q + 4q^2 + q^3.

If Q = 5, then:

AFC = FC/Q = 30/5 = 6.

AVC = VC/Q = (3q + 4q^2 + q^3)/q = 3 + 4*5 + 5^2 = 48.

ATC = AFC + AVC = 6 + 48 = 54.

MC = TC' = 3 + 8q + 3q^2 = 3 + 8*5 + 3*25 = 118.

b) The ATC curve is the sum of the AVC and AFC curves. AFC curve is decreasing, because FC is constant, and AVC and ATC curves decrease until they intersect with the MC curve, and after that they start to increase.

c) the relationship between marginal cost (MC) and marginal product (MP) is such that when MC decreases, then the MP increases and inversely.

The law of diminishing marginal returns states, that with the increase in quantity produced the marginal returns of the every additional unit of input decrease. In this case when MC increase, then MP decreases and inversely.

If Q = 5, then:

AFC = FC/Q = 30/5 = 6.

AVC = VC/Q = (3q + 4q^2 + q^3)/q = 3 + 4*5 + 5^2 = 48.

ATC = AFC + AVC = 6 + 48 = 54.

MC = TC' = 3 + 8q + 3q^2 = 3 + 8*5 + 3*25 = 118.

b) The ATC curve is the sum of the AVC and AFC curves. AFC curve is decreasing, because FC is constant, and AVC and ATC curves decrease until they intersect with the MC curve, and after that they start to increase.

c) the relationship between marginal cost (MC) and marginal product (MP) is such that when MC decreases, then the MP increases and inversely.

The law of diminishing marginal returns states, that with the increase in quantity produced the marginal returns of the every additional unit of input decrease. In this case when MC increase, then MP decreases and inversely.

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