This ''equalizing difference'' equation determines a college-high-school wage ratio that equalizes present values of a high school educated worker and a college educated worker.

The idea is that lifetime earnings somehow adjust to make a new high school worker indifferent between going to college and not going to college but instead going to work immmediately.

The idea is that lifetime earnings somehow adjust to make a new high school worker indifferent between going to college and not going to college but instead going to work immediately.

(The job of the "other equations" in a more complete model would be to describe what adjusts to bring about this outcome.)

We suppose that $R, \gamma_h, \gamma_c, T$ and also $w_0^h$ are fixed parameters.

We start by noting that the pure equalizing difference model asserts that the college-high-school wage gap $\phi$ solves an

"equalizing" equation that sets the present value not going to college equal to the present value of going go college:

"equalizing" equation that sets the present value not going to college equal to the present value of going to college:

$$

plt.show()

```

Notice how the intitial wage gap falls when the rate of growth $\gamma_c$ of college wages rises.

Notice how the initial wage gap falls when the rate of growth $\gamma_c$ of college wages rises.

The wage gap falls to "equalize" the present values of the two types of career, one as a high school worker, the other as a college worker.

of a successful entrepreneur's earnings to a worker's earnings.

We'll find that as $\pi$ decreases, $\phi$ increases, indicating that the riskier it is to

be an entrepreuner, the higher must be the reward for a successful project.

be an entrepreneur, the higher must be the reward for a successful project.

Now let's adopt the entrepreneur-worker interpretation of our model

Thus, as with our earlier graph, we find that raising $R$ increases the initial college wage premium $\phi$.

Compute $\frac{\partial \phi}{\partial T}$ and evaluate it a default parameters

Compute $\frac{\partial \phi}{\partial T}$ and evaluate it at default parameters

```{code-cell} ipython3

ϕ_T = ϕ(D, γ_h, γ_c, R, T, w_h0).diff(T)