The table above shows Randy's Shirts' short-run production function. Randy hires workers at a wage rate of $50 a day and his total fixed cost is $100

a) What is the marginal product of the 3rd worker?
b) What is Randy's average fixed cost if 48 shirts are produced?
c) What is Randy's average variable cost if 56 shirts are produced?
d) What is Randy's marginal cost of producing the 52nd sweater?
e) What is Randy's average total cost if 48 sweaters are produced?

a) When the 3rd worker is hired, output increases from 36 to 48, an increase of 12 shirts per day. So the marginal product of the 3rd worker is 12 shirts per day.
b) Average fixed cost is total fixed cost divided by the output produced. Total fixed cost is $100, so Randy's average fixed cost is $100/48, which is $2.08 per shirt.
c) Average variable cost is total variable cost divided by the output produced. To produce 56 shirts, Randy needs 4 workers. So Randy's total variable cost is $50 × 4, which is $200. Then, his average variable cost is $200/56, which is $3.57 per shirt.
d) The 52nd sweater is produced when the 4th worker is hired and the output increases from 48 to 56 shirts. The marginal cost of producing these additional 8 shirts is the cost of employing the additional worker, $50. So the marginal cost of producing the 52nd shirt is $50/8 = $6.25. Alternatively, the total cost of producing 48 shirts is $100, the fixed cost, plus 3 × $50, the variable cost, which is $250. And the total cost of producing 56 shirts is $100, the fixed cost, plus 4 × $50, the variable cost, which is $300. Then the marginal cost equals the change in the total cost divided by the change in output, or $50/8, which is $6.25.
e) Average total cost is total cost divided by the output produced. Total cost is fixed cost plus variable cost. Randy's fixed cost is $100. To produce 48 shirts, he needs 3 workers, so his total variable cost is $50 × 3 = $150. Randy's total cost is $100 + $150 = $250. Then his average total cost is $250/48, which is $5.21.