1. ICE CREAM PRODUCTION Suppose that a person sells ice cream from a cart on the street. Labor input is denoted by L and ice cream output is denoted by Y. The relationship between labor input and ice cream output (i.e., the person's production function) is given by Y = [1/? (This means that the person can sell 3 units using 9 minutes, can sell 4 units using 16 minutes, and so on. This also implies [ = 12.). The equilibrium wage rate is given by w = 3 per minute, which reflects the opportunity cost of the person's time, and the market price of ice cream is p. Assume that the market for ice cream is perfectly competitive and that all ice cream carts are identical. There is a fixed cost of F that the person has to pay to rent the cart (and whatever ice cream sold). (a) What is the ice cream cart's total cost function C(Y)? (Hint: the cart's cost is the fixed cost plus variable cost - in this case, the person's wage bill and for simplicity we assume the ice cream sold is already included in the fixed cost and doesn't change with the amount sold.) (6 points) (b) What is the ice cream cart's marginal cost function MC(Y)? (Hint: recall that the marginal cost function gives the additional cost of producing one more unit.) (6 points) (c) What is the ice cream cart's average (total) cost function ATC(Y)? (Hint: the average cost function represents the per unit cost of both fixed cost and variable cost in production.) (6 points) (d) Assume that the price of ice cream is 24 and that F = 40. How long will the person work? How many ice creams will the person sell? (Hint: find the the optimal level of production implied by profit maximization. Then check whether this level of output yields positive profits.) (8 points) (e) Assume that the price of ice cream is 18 and that F = 40. How long will the person work? How many ice creams will the person sell? (6 points) (f) Find the price level p* for which the person sells nothing whenever p p (ie. enters the market), as a function of the fixed cost F. (Hint: at this price level, profits are zero.) (8 points)(g) How is the price level p' found in the previous part related to the ice cream cart's average total cost? (8 points) (h) What is the ice cream cart's supply function? (8 points)