In this paper annual Canadian exploration data are used to estimate a multiple-output translog exploration cost function. A new definition of depletion is introduced and its estimated coefficient is found to be statistically significant. Another novel feature is the application of Monte Carlo integration to ensure the estimated cost function satisfies concavity and monotonicity. The *fitted cost function parameters are then used to obtain estimates of the marginal costs of exploration for oil and gas. Our estimated marginal exploration costs are smaller than previous* studies' because we have allowed for technical progress which offsets the depletion effects. These marginal cost estimates are employed, along with previous estimates of exploration rents, to measure resource scarcity. We find some evidence for the increased scarcity of oil and gas in Alberta- • For oil there is a 10.07. per year increase in scarcity along' the trend line while for natural gas there is a 1.87. per year increase in scarcity along, the Crend line.