Suppose there is a single consumer with U = Sl, where S is steaks and l is leisure time.
The Consumer is endowed with one unit of leisure time, and the production for steaks is S = l / c , where c >0 is a constant.
Assume that the government can observe the leisure that is consumed. It taxes leisure consumed at t per unit of leisure and returns the collected ‘revenue’ to the consumer.
Find the equilibrium consumption of steaks and leisure, and calculate the welfare loss (in terms of utility) of this tax. Explain your answer in words with reference to an appropriate diagram.