Under the zero lower bound the stimulating policies are conducted mostly by the fiscal authorities due to inefficiency of the traditional monetary policy. Recent research showed that in the borrower-saver framework the government expenditure multiplier can be significantly higher under the zero lower bound than under a positive interest rate. This paper explores the fiscal multiplier in the excess-savings liquidity trap in the extended framework which incorporates productive along with utility-enhancing government expenditures. The share of public investment in total expenditures and its productivity decrease the multiplier under the zero lower bound and increase it under a positive interest rate. In the former case, the higher share of liquidity-constrained borrowers weakens the negative effect of public investment, with an opposite impact in the latter case. An assumption about the two types of public expenditures intensifies the non-linear impact of the borrowers' share on the multiplier: the multiplier can become negative under zero lower bound for the sufficiently high share of borrowers.