function grad = economics_vk_grad(parameters, expenditure, income)

% function to compute gradients from L2 error for fit of v(t) and k(t) 
% parameters in consumption deprivation model.

V = parameters(1);
K = parameters(2);

Z = V*income./(K + income);

err = dist2(expenditure, Z);

% now do the gradients
grad_V = sum(2*(expenditure - Z).*(income./(K + income)));
grad_K = sum(2*(expenditure - Z).*-Z./(K + income));

grad = -[grad_V,grad_K];

end