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Let us rewrite the code, so that every human eye can digest the question:

var( 'r,B,a,y,k,d,c,N,A,theta' )
eq1 = r == B * ( a*y / k + 1 - d )
eq2 = y == c + k * (r-1+d)
eq3 = (1-a)*(y/N) == (1-theta) / theta * c / (1-N)
eq4 = y == A * k^a * N^(1-a)
h   = solve( [ eq1, eq2, eq3, eq4 ], [y,c,N,k] )


Now we will look closer to the eq4 and see that variable k to the power... variable a. The doc of solve refers to algebraic equations.

Docstring: Algebraically solve an equation or system of equations (over the complex numbers) for given variables. Inequalities and systems of inequalities are also supported.