Basing this on Nick Rowe's post on Keynes' General Theory (Chapter 3). It appears to be set up as an information transfer market

\frac{W}{P} : Y \rightarrow L

$$

with real wages $W/P$, real output $Y$ and employed labor force $L$ so that

$$

\frac{W}{P} = \frac{dY}{dL} = \frac{1}{\kappa} \; \frac{Y}{L}

$$

from the basic information transfer model. Looking at constant $Y = Y_{0}$, we have

\frac{W}{P} = \frac{1}{\kappa} \; \frac{Y_{0}}{\langle L\rangle}

$$

where $\langle L\rangle$ is the expected value of the labor supply. This is Rowe's second equation ("classical labor demand"), written as $W/P = MPL(L)$ and subsequently $W/P = 1/L$. Ours is technically $W/P = c/L$ where $c$ is a constant. Solving the differential equation, we obtain

\Delta Y \equiv Y-Y_{ref} = \frac{Y_{0}}{\kappa}\log \frac{\langle L\rangle}{L_{ref}}

$$

where $ref$ refers to reference values of the variables $L$ and $Y$. This is analogous to Rowe's first equation ("classical production function"), written as $Y = f(L)$ and subsequently $Y = \log L$. Ours is technically $Y = c_{1} \log L + c_{2}$ where the $c_{i}$'s are constants.

Rowe's third equation $W/P = MRS(L, Y)$ follows from looking at constant $L = L_{0}$ so that we have (solving the differential equation again):

\frac{W}{P} = \frac{1}{\kappa} \; \frac{\langle Y\rangle}{L_{0}}

$$

$$

\Delta L \equiv L-L_{ref} = \kappa L_{0} \log \frac{\langle Y\rangle}{Y_{ref}}

$$

where we can eliminate $\langle Y\rangle$ to produce (after some re-arranging)

$$

\log \frac{W}{P} = \log \frac{Y_{ref}}{\kappa L_{0}} + \frac{\Delta L}{\kappa L_{0}}

$$

Rowe's form is $W/P = Y/(1-L)$, but I'm not entirely sure what the $1$ is supposed to mean (full employment?); however we basically obtain this if we take the log of both sides

\log \frac{W}{P} = \log Y + \log \frac{1}{1-L}

$$

and expand around $L = L_{ref}$ so that

$$

\log \frac{W}{P} = \log Y + \log \frac{1}{1-L_{ref}} + \frac{L - L_{ref}}{1-L_{ref}} + \cdots

$$

$$

\log \frac{W}{P} \simeq \log Y + \log c + c \Delta L

$$

Of course, $W/P : Y \rightarrow L$ is a terrible model (Keynes' disagreed with at least part of it) ... here's this model compared to data:

A much more successful market would be $P : W \rightarrow L$:

Where the equations that define the supply and demand curves are (respectively):

$$

\log P = - \log \frac{\kappa L_{0}}{W_{ref}} + \frac{\Delta L}{\kappa L_{0}}

$$

$$

\log P = \log \frac{W_{0}}{\kappa L_{ref}} - \frac{\kappa \Delta W}{W_{0}}

$$

You would plot them as functions of $\Delta L$ or $\Delta W$ so that $P \sim \exp(1-\Delta W)$ or $P \sim \exp(\Delta L-1)$ and they look like this:

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