Answer to Question #165783 in Microeconomics for Olayinka Dele

Question

ricardo produces widget, using (L) as input labor and (k) machine. His production function is given by the following equations

q= 10k^2/3 + L^1/2

1) what type of return to scale does ricardos production function and exhibits? Explain

2) at the end of last year, Ricardo bought his only machine for $1000. He will use the machine for 5 years , after which the machine will have no value . Ricardo will calculate depreciation linearly (depreciation will be 20% of the total value of the machine per year ). This machine has no other use beside ricardos production of widget and at this moment Ricardo cannot buy any more machine

what is Ricardos annual fixed cost of production? Is the fixed cost sunk or not ? Explain

Answer 1

1) The production function exhibits an increasing returns to scale.

Explanation:

Increasing returns to scale refers to a situation where the rate of change of firm's output is higher than that of inputs.

In Ricardo's case, we find the total amount of returns to scale by adding the exponents 2/3 and 1/2 to get 7/6 which is a value greater than 1.

When sum of exponents is larger than 1, we therefore say that Ricardo's firm has an increasing returns to scale.

2) Annual Fixed cost is the depreciation of each year. The machine depreciates at 20% of initial value of the machine. Therefore Annual fixed cost would be

Hence annual fixed cost is $200.

It is a sunk cost as Recardo already spend it and can not recover anymore.