Microeconomics: A Comprehensive Theory of Costs ECO2003

Comprehensive practice questions covering short-run and long-run cost theory, productivity measures, and Lagrangian optimization based on Microeconomics lecture notes.

What establishes the link between the quantities of physical inputs and the financial cost of production?

The transition from the theory of production to the theory of costs.

In the short run, what defines the measure of Average Product of Labour ($APL$)?

$$APL = \frac{Q}{L}$$

How is the Marginal Product of Labour ($MPL$) mathematically defined?

It is the first derivative of the production function: $MPL = \frac{dQ}{dL}$

What does the Law of Diminishing Marginal Returns state?

As equal increments of a variable input (labour) are added to a fixed input (capital), the resulting increments in total output will eventually decline.

Why do short-run costs eventually begin to rise technically?

Due to the decline in productivity when fixed capital is over-utilised and workers begin to crowd the workspace.

What is the reciprocal relationship between Marginal Cost ($MC$) and Marginal Product of Labour ($MPL$)?

$$MC = \frac{w}{MPL}$$

What is the relationship between Average Variable Cost ($AVC$) and Average Product of Labour ($APL$)?

$$AVC = \frac{w}{APL}$$

What happens to Marginal Cost ($MC$) when Marginal Product of Labour ($MPL$) is at its maximum?

Marginal Cost ($MC$) reaches its minimum.

In short-run cost categories, how is Fixed Cost ($FC$) formulated?

$FC = rK_0$, where $r$ is the rental price and $K_0$ is the fixed amount of capital.

How is Total Cost ($TC_Q$) calculated in the short run?

$$TC_Q = FC + VC_Q = rK_0 + wL$$

In the provided Laundromat example, if $r = R0.25$ and $K = 120$, what is the Fixed Cost?

$FC = R30$ per hour.

Describe the geometry of the Variable Cost ($VC$) curve during the Increasing Returns Phase.

The curve is concave because variable cost grows at a diminishing rate.

How is the Total Cost ($TC$) curve related to the Variable Cost ($VC$) curve graphically?

The $TC$ curve is the $VC$ curve shifted vertically upwards by the amount of the Fixed Cost ($FC$).

What is the formula for Average Fixed Cost ($AFC_Q$)?

$$AFC_Q = \frac{FC}{Q} = \frac{rK_0}{Q}$$

Why does Average Fixed Cost ($AFC$) decline continuously as output increases?

Because the constant overhead is spread over a larger number of units.

What is the Marginal Rate of Technical Substitution ($MRTS$)?

It is the absolute slope of the isoquant, defined as $\frac{MPL}{MPK}$, representing the technological rate of exchange between capital and labour.

What is the fundamental tangency condition for long-run cost minimisation?

$$\frac{MPL}{MPK} = \frac{w}{r}$$

What does the Expansion Path represent?

The locus of optimal input combinations for every possible level of output, given a fixed set of factor prices.

How is the Long-Run Average Cost ($LAC$) curve defined in relation to short-run curves?

It is the lower envelope of all possible short-run average cost curves.

In a capital-intensive disequilibrium where $MRTS > \frac{w}{r}$, which input should the firm hire more of to increase efficiency?

The firm should hire more labour because the marginal product per Rand spent on labour ($\frac{MPL}{w}$) is greater than that of capital ($\frac{MPK}{r}$).

In a labour-intensive disequilibrium where $MRTS < \frac{w}{r}$, what is the iterative adjustment process?

The firm must substitute labour for capital by shedding excess labour and investing in machinery until $MRTS = \frac{w}{r}$.

What variable is introduced in the Lagrangian method to convert a constrained problem into an unconstrained one?

The Lagrange multiplier, denoted as $\text{ω}$.

Given $Q = 10L^{0.5}K^{0.5}$, $w = R50$, and $r = R200$, what is the expansion path equation?

$$L = 4K$$

In the shift in relative prices example, if the wage increases to $w = R200$ and $r = R200$, what is the new optimal labour-to-capital ratio?

A 1-to-1 ratio ($L = K$).