Section II: Industry Case Study

Business Leverage & Vertical Effects of Market Power

$(40$ points$)$

Brett owns a brewery called "Beach Light Brewing" located on the Jersey shore. He is a purely self$-$interested business manager who will always make logical$,$ risk$-$neutral, and profit$-$maximizing decisions. There are many workers available in the competitive local labor market who are all capable of performing any job at BLB$,$ with only one exception: Casey is the only highly skilled beer$-$maker in the area capable of working as Chief Brewer, and this supervisor position must be filled in order to produce any beer with any number of workers. Casey's only desired compensation is equity stake in the BLB business instead of a salary. Assume that all other workers are identical and anyone who chooses to work at BLB must work for exactly $10$ hours a day and values their leisure time at a constant rate of $$15\mathrm{.}99$ per hour.

BLB produces two product types: lagers $($ L $)$ and ales $($A$).$ The variable cost of all capital inputs for production $($including ingredients, materials, depreciation, etc.$)$ is $$1$ per lager and $$3$ per ale. With Casey overseeing production, each worker can make either $12$ lager units per hour or $9$ ale units per hour, and BLB only has room for a maximum of $10$ workers in addition to Casey supervising. BLB can sell lagers for $$10$ each to Vunion, a large wholesale distributor which sells beer to retail stores all over the US$.$ Vunion will buy any amount of lagers from BLB for a fixed rate of $$10$ per unit but will not buy ales. BLB also has the option to sell lagers and ales on site directly to consumers at the brewery based on market demand. State regulations, however, require that breweries choose to sell each specific product type either only through distributors or only directly to consumers. The total daily fixed cost of operation for BLB is $$2000.$

Assume there are numerous competing breweries in the local market which sell lagers and ales directly to consumers on site and BLB is not large or powerful enough to influence these market equilibrium prices. Local prices per unit are given by the following equations, and you do not ever need to account for BLB$\text{'}$s actions in terms of the quantity values or individual effect on equilibrium calculations here:

$((]\}[$

$P{s}^A=\frac{q^A}{200}$

$PsL=q\frac{L}{800}$

a$)$ Draw a diagram illustrating the daily Production Possibilities Frontier for BLB$.$

b$)$ What is the local market's equilibrium unit price ana tota quanuty for ales?