# Tangent Curves to Linear Functions (Wages and Cobb Douglas)

**URL:** <https://discourse.julialang.org/t/tangent-curves-to-linear-functions-wages-and-cobb-douglas/37377>\
**Category:** Optimization (Mathematical)\
**Created:** [April 11, 2020, 3:18am UTC](https://discourse.julialang.org/t/tangent-curves-to-linear-functions-wages-and-cobb-douglas/37377 "2020-04-11T03:18:53Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![brett\_knoss](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/brett_knoss/32/13050_2.png) [@brett\_knoss](https://discourse.julialang.org/u/brett_knoss)\
**Post date:** [April 11, 2020, 3:18am UTC](https://discourse.julialang.org/t/tangent-curves-to-linear-functions-wages-and-cobb-douglas/37377/1 "2020-04-11T03:18:53Z")

</div>

```julia
using Gnuplot, Gaston, Convex, SCS

L= 0:600
K=0:600
C=0:600
Q=0:8000

contour(K, L, (K,L)->.1*K^.5*L^1.5, xlabel="Leisure", ylabel="Consumption",labels=false)
#same function as a contour graph for somereason, doesn't reach

#now I need to add wages
problem = minimize(sumsquares(A * x - y), [x >= 0])
# looks about right, except if I want W*h-y, then I need to change variables
# " " W*168-y, then I have a constant as x

```

Can I use the above to find where each wage rate (K=168-L\* K/L) is tangent to a Utility curve?