A competitive firm has the following short-run cost function: c(y)=0.5y^3-y^2+2y+3. Market price of each unit of output is $2. a) Write down equations for the firm's average variable cost function and the firm's marginal cost function.

b) At what level of output is average variable cost minimized? c) Given the market price of the output above, what is the profit maximizing amount of output? Or how many units of output should the firm produce so that his profit can be maximized? d) How much profit does the firm make when it maximizes profits? Determine firm's supply decision in both short run and long run.