A firm in the state of Karnataka in India can source one of its factors of production either within the state, \(F_{K}\), or from the neighboring state of Maharashtra, \(F_{M}\). Assume the quality and rental price of the input is identical in both states, \(r=₹ 1,000\) per hour, and there is no significant difference in the cost of transporting the input for use in the firm's production facilities. However, the rate of value-added tax in Karnataka is \(t_{K}=14.5 \%\), while it is 2 percentage points lower in Maharashtra, \(t_{M}=12.5 \%\). Use an isocost-isoquant diagram to explain how the cost-minimizing firm would likely respond to this tax rate differential.