We document the presence of asymmetric business cycles in both regular and contract labour markets in India, investigate the role of nominal wage rigidities in accounting for these asymmetries, and study optimal inflation policy in such a milieu. Using data from Annual Survey of Industries, we find that (i) the growth of regular employment is negatively skewed while that of contract employment is positively skewed, and (ii) the nominal wage growth of regular workers is positively skewed while that of contract workers is negatively skewed. To understand the policy implication of asymmetric labour adjustment, we first show that a workhorse business cycle model needs to be augmented with asymmetric wage adjustment costs for both regular and contract labour to match the observed asymmetries in employment. Our model further suggests that the presence of contract labour reduces the optimal level of grease inflation required in the economy as it relaxes the constraint of downward nominal wage rigidity.