Microeconomics,, 16th Canadian Edition

31. The “rule of 72” says that any sum growing at the rate of X
    percent per year will double in approximately years. For
    two sums growing at the rates of X percent and Y percent per
    year, the difference between the two sums will double in
    approximately years. The rule of 72 is only an
    approximation, but at low annual rates of growth it is extremely
    accurate.


32. A simple example of a production function is
    This equation says that to find the amount of GDP produced,
    multiply the amount of labour by the amount of capital, take the
    square root, and multiply the result by the constant z, which is a
    technology parameter. This production function has positive but
    diminishing marginal returns to either factor. This can be seen by
    evaluating the first and second partial derivatives and showing
    the first derivatives to be positive and the second derivatives to
    be negative.
    For example,

and

33. The production function displays constant
    returns to scale. To see this, multiply both L and K by the same

72 /X

72 /(X−Y)

GDP=z(LK)

∂G∂KDP = z⋅L > 0

1 / 2

2 ⋅K^1 /^2

∂ = < 0

(^2) GDP
∂K^2
z⋅L^1 /^2
4 ⋅K^3 /^2
GDP=z(LK)^1 /^2