Question

1. Schmutz Auto Wash provides car washes. Its production function is ? = 2?^1/2(? - 1)^1/2
where ? is cars washed per day, ? is daily hours of labor input, and ? is daily usage of capital inputs. The price of a unit of capital input is $48. The price of a unit of labor input is $16. In the short run, Schmutz has one unit of capital input installed (so ? = 1).

a). Find Schmutz’s short run daily total cost function, short run daily variable cost function, and short run daily fixed costs.

b). Find Schmutz’s short run marginal cost function, short run average variable cost function, and short run total cost function.

c). Suppose that the market for car washes is perfectly competitive and the going market price of a car wash is ?. Find Schmutz’s short run daily supply function, including its shutdown price.

d). Find Schmutz’s short run daily quantity supplied, producer surplus, and profit if ? = 40.

Answer 1