S. Klepper, Economics 73-100, Fall 2011
If wages rise by 10% and labor is the only variable cost of production, then total variable costs must rise by 10% at every level of output. This in turn implies that marginal and average variable costs rise by 10% at every level of output. Since fixed costs rise by 30%, average total cost rises by more than 10% at every level of output.
The (short-run) market supply curve is based on firm marginal cost curves. With marginal cost increasing by 10% at every level of output, the market supply curve must shift to the left, as pictured in the figure below, where S0 and S1 denote the supply curve before and after the increase in costs. The original price and output are denoted by p0 and q0. The new price, denoted by p1, is equal to 1.1 times p0. As the figure indicates, at the new price, the quantity supplied is q0, the original output. The quantity supplied is the output where marginal cost equals price. At q0, the marginal cost has increased by 10%. With price also rising by 10%, marginal cost equals the new price at q0, so firms continue to supply their original output of q0. In the short run, the break-even price at which it is profitable to supply a positive level of output equals the minimum average variable cost of production. With average variable cost rising by 10% at every level of output, the minimum value of the average variable cost must rise by 10% and thus the break-even price must rise by 10%. Since the price of milk increases by 10%, this implies that any firm that found it profitable to supply a positive level of milk before the cost and price increases will find it profitable to continue to supply a positive level of milk after the cost and price increase and thus will not shut down.
Based on this description, the answers to the individual questions are: