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02 (a) 7 . carpenter who makes tables. His production function for the number of tables he I l produces is f (x1 , x2) = ac]E :621 where an is the amount of labour and x2 is the amount of wood he uses. His tables sell for $40 per unit. Labour costs $20 per unit and wood costs $10 per unit. That is, the variable cost to production is 203:; + 10x2. There is also an additional fixed cost for his workshop of $10 that needs to be paid regardless of whether any output is produced. What is the profit-maximizing amount of each input to use? How much does the firm produce when it is profit-maximizing? How much profit does the rm make? 02 (b) The government introduces a new tax of 10% profits. What is the after tax profit function? How much of each input does the rm use? How much prot does the firm make after tax