Answer to Question #164816 in Microeconomics for Omas

Question

Richardo produces widgets, using as input labour (L) and machines (K) . His production function is given by the following equation . q = 10K^(2/3)  L^(1/2).

a). what type of returns of scale does richardo production function exhibit? Explain?

b). At the end of last year, Richardo bought his only machine for $1,000. He will use the machine for 5 years, after which the machine will have no value. Richardo will calculate depreciation linearly ( depreciation will be 20% of the total value of the machine per year). This machine has no other use besides Richardo's production of widgets and at this moment, Richardo cannot buy any more machines.

What is Richardo's annual fixed cost of production? Is the fixed cost sunk or not? Explain?

Answer 1

a)

$$\frac {\delta q}{\delta K}=\frac {20}{3}(\frac{L}{K})^{\frac{1}{3}}$$

$$\frac {\delta q}{\delta L}=\frac {10}{3}(\frac{K}{L})^{\frac{2}{3}}$$

b)

1-st year

$$0.2\times1000=200$$

$$1000-200=800$$

2-nd year

$$0.2\times800=160$$

$$800-160=640$$

3-d year

$$0.2\times640=128$$

$$640-128=512$$

4-d year

$$0.2\times512=102.4$$

$$512-102.4=409.6$$

5-th year

$$0.2\times409.6=81.92$$

$$409.6-81.92=327.68$$

The fixed cost is unpaid. This is due to the fact that the cost of equipment has been decreasing every year.