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1 vote
0 answers
29 views

Toy model equilibrium calculation: How a small system's firm determines wage and price?

I am trying to model a small system, with limited population and a single firm. Personally I have no economic background but only taken a simple microeconomics course and I am quite interested in ...
DongAlpha's user avatar
0 votes
0 answers
37 views

Modelling the optimal mix of labour

I am trying to model the profit maximization decision of a firm that uses two types of labor, workers A and workers B. I started by drawing the marginal product and marginal cost curves (lines, for ...
Mikhail's user avatar
5 votes
3 answers
2k views

Cobb-Douglas Production Function - Finding units of labour to maximise production

Given production function $f(L,K)=16L^\frac{1}{4}K^\frac{3}{4}$, where each unit of labour costs £50 and each unit of capital costs £100 and you have a budget of £500,000. Find the number of units of ...
James Burton's user avatar
6 votes
1 answer
111 views

Doraszelski and Jaumandreu (2018) Intuition

Doraszelski and Jaumandreu (2018) estimate a CES production function with two forms of productivity shocks (1) labor augmenting and (2) Hicks neutral. They claim that the increase in labor augmenting ...
Michael Gmeiner's user avatar
4 votes
1 answer
129 views

Walras Law in a production economy with fixed costs

Consider a price taking firm with fixed costs $fc \geq 0$: \begin{align*} \Pi &= \max_{n^D} \left\{ P_c F(n^D) - w\times n^D - fc \right\} \end{align*} A representative household owns this firm:...
Albert Zevelev's user avatar
3 votes
1 answer
83 views

Does labor negatively affect output (from empirical perspective)?

I am estimating Cobb-Douglas production function for US using time series framework: $$Y_t=A_t \times L_t^\alpha K_t^\beta $$ where $Y$ is output, $A$ is $TFP$, $L$ is labor and $K$ is capital. After ...
Duo's user avatar
  • 121
4 votes
2 answers
370 views

Convenient S-shaped production function (i.e. with IRS and DRS) to derive a discontinuous demand for labor

Let say that a firm produces a commodity using only one input (i.e. Labor if we suppose to be in the very short run). Then we have a general production function of the following form $y=f(L)$, for $L≥...
Alessandro's user avatar
3 votes
3 answers
694 views

Cobb-Douglas production function, given $w$ get $r$ regardless of input levels. Why?

There is a market economy with technology given by: $$Y = K^\alpha L^{1-\alpha} \tag{1}$$ Firms behave competitively and input prices are: $$r = \alpha K^{\alpha-1}L^{1-\alpha} = \alpha(\frac{L}{K})...
Tecon's user avatar
  • 129