Intermediate Micro Theory Firm Supply

We assume firms make decisions to maximize profits π(q) = pq – c(q) Therefore, how much should a profit maximizing firm supply of that output?

Firm Supply Profit maximizing firm wants to maximize difference between total Revenue and Total costs. This will be where slope of cost function (i.e. MC) equals the price of the output Or equivalently, where the slope of the profit function equals zero (“First Order Condition” or FOC) $ pq C(q ) q* $ π(q)= pq-C(q)

Firm Supply So a necessary condition for profit maximization is that chosen output (q*) is such that: MC(q*) = p What if MC(q*) = p at more than one q? What if p < AC(q*) (where q* is such that MC(q*) = p)? What if p < AVC(q*) (where q* is such that MC(q*) = p)? Given these results, can we derive the firm’s supply curve?

Firm Supply So, in short run, Firm supply curve is implicitly given by MC(q) curve above AVC(q) curve. What about in Longer run? Before moving on to analytic details, what will total profit look like graphically, for any given p? $ q MC(q) AC(q) AVC(q) p

Firm Supply Analytically Analytically, short-run firm supply curve derived as follows: Given any price p, let q * (p) to be such that MC(q*(p)) = p Then: q s (p) = 0 if MC(q*(p)) < AVC(q*(p)) = q * (p) if MC(q*(p)) > AVC(q*(p))

Firm Supply Analytically Ex: Consider Firm’s (short-run) cost function from before: C(q) = q 4 / What will be equation for firm’s supply curve?

Long-Run vs. Short-Run Supply Curve Recall from before that the Short-run MC(q) curve was the MC(q) curve that held when at least one factor was fixed at some level. Alternatively, in Longer-run, more factors become variable. This meant any Short-run MC curve lies above the Longer-run MC curves at any given q. What does this imply about relative slopes of short-run vs. longer-run supply curves?

Bringing it all together: Suppose a firm producing widgets operated using a Cobb-Douglas technology such that q = L 0.25 K 0.25, where the going wage rates are w L = $12/hr and w K = $12/hr. How much would a profit maximizing firm supply if each widget could be sold for $144? How about if it could be sold for $192? How would we sketch this all graphically?

Bringing it all together: Scale Effects vs. Substitution Effects Consider a price change for one of the inputs in the production of some output. Substitution Effect (for input x 1 ) – change in firm’s demand for x 1 due to change in cost-minimizing way to produce any given level of output. Scale Effect (for input x 1 ) – change in firm’s demand for x 1 due to change in optimal level of output.

Example: Minimum Wage Laws Advocates for increasing minimum wage cite these laws as effective tools for fighting poverty. What might be a concern when increasing minimum wage in competitive markets?