Question

Brice is a seller of lemonade operating in the perfectly competitive lemonade stand market Brice's short-run total cost curve is given by STC(Q) = 400 2Q + 0.5Q2, where Q is the number of cups of lemonade sold per month. (a) What is the equation for the average variable cost (AVC)? (b) Assuming all fixed costs are sunk, what is the shutdown price for Brice? In this case, what is Brice's short-run supply curve? (c) Assuming $200 of the fixed costs are sunk and the rest of the fixed costs are nonsunk ECON 201 what is the shutdown price for Brice? In this case, what is Brice's short-run supply curve?

Answer 1

Short run total cost STC = 400 + 2Q + 0.5Q^2

a) AVC is VC/Q and so AVC = 2 + 0.5Q

b) When the fixed cost is entirely sunk, the shut-down price is minimum of average cost as well as the minimum of average variable cost because the fixed cost is then not considered in cost function. Hence we have AC = AVC = 2 + 0.5Q and minimum AVC is $2. The shut down price is $2. Marginal cost is MC = 2 + Q and so supply function is Q = P - 2 where P > 2.

c) In case the fixed cost is partially sunk and partially non-sunk (avoidable) then we consider only the partially non-sunk cost. Hence the relevant average cost function is AC = 200/Q + 2 + 0.5Q. It is minimum when -200/Q^2 + 0.5 or Q = 20 and so AC = 200/20 + 2 + 0.5*20 = $22. This is the shut down price. Now the supply curve is Q = P - 2 where P > 22