Equilibrium in the Goods and Labor Markets

Workers

Let labor supply be

Ls=16-(1/(3w))

Consumers

Let demand for goods be:

yd=7-p

Firms

Production

production = y==(L^(1/2))

Conditional Factor Demand

cfd = L /.Solve[production,L][[1]]

Total Variable Cost

TVC=w*L /. L -> cfd

Marginal Cost

MC= D[TVC,y]

Supply

ys = y /. Solve[MC==p,y][[1]]

Labor Demand

Ld = cfd /. y -> ys

Equilibrium Conditions

Goods Market Equilibrium

goods = yd == ys

Labor Market Equilibrium

labor = Ld==Ls

General Equilibrium (sort of general, really still partial)

{(SuperStar[p]),(SuperStar[w])} = Solve[{goods,labor},{p,w},Reals][[3]]//N

Graph the Labor Market

inverselaborsupply=w/.Solve[L==Ls,w]

inverselabordemand=w/.Solve[L==Ld,w][[2]]/.(SuperStar[p])

Plot[{inverselabordemand,inverselaborsupply},{L,0,16}]