## The price–cost mark- up in the UK: a long- run perspective NIC HO lA S CRAFTS A ND TeR eNC e C . MIllS

Here w, p, y and n denote the logarithms of W, P, Y and N, respectively, and m is the (log of the) mark-up, defined as

m e e

= −

log 1

(12.6)

Since the mark-up is a function of the elasticity of demand e, any change in the mark-up will reflect a change in this elasticity or, equivalently, a change in competition. Equation (12.5) can be rewritten as the factor-demand equation for labour

y n p w= − −( ) + −( ) − −( ) +s s h s a sm1 1log (12.7) Subject to the capital accumulation identity

K K It t t+ = −( ) +1 1 δ (12.8) the factor-demand equation for capital is derived as

y k r= + − +s s a smlog (12.9)

where r is the (log of the) real user cost of capital (RCC). The labour and capital factor-demand equations should hold in long-run equilibrium: note that from the assumption that technical progress is labour-augmenting the latter equation does not contain h. A simple transformation of (12.7) yields

m s s

h a= −( ) + −( ) + −

− −( ) + −( )p w y n y n1 1log (12.10)

With a assumed to be fixed, this equation has the simple interpretation of

markup inverse labour share labour productivity te= + −

× −1 s

s chnical progress( )

markup inverse labour share labour productivity te= + −

× −1 s

s chnical progress( )

In a steady state the mark-up and labour share will not vary over time and technical progress may be interpreted as ‘trend’ labour productivity. When labour productivity is above (below) this trend, the mark-up is then rising (falling) (conditional on the labour share). The lower s is (the harder it is to swap between capital and labour in production) the bigger any change in the mark-up will be. However, the mark-up itself is an unobserved variable. While it is often assumed to be constant when models of this type are estimated, this obviously imposes steady-state behaviour. As an alternative, m might be modelled by including other variables such as capacity utilisation or import prices, essentially ‘adding on’ these variables to a constant. As there is, in general, no reason to believe that movements in the mark-up must correspond exactly to movements in these variables, a less restrictive approach in which the mark-up is allowed to vary over time in a non-dependent framework would be attractive. Similar considerations would also apply to technical progress. Such time dependencies must obviously be related to the behaviour over time of the observed variables in (12.7) and (12.9), the (inverse) labour-output and capital-output ratios, y – n and y – k, the price to labour cost ratio p – w and the real cost of capital, r, which naturally leads us on to a discussion of the available data.