Chapman University Profit Function and Its Graph Exercises
They are on page 27 and page 34. The rest of the documents are just lecture materials. Questions generally correlate to the few paragraphs ahead of them.
Problem 11 If an agent purchases x units of X and y units of Y the agent’s expenditure is
px x + py y. In our example we have fixed the price of X at px = 1 and simplified the notation
for py to p. With these prices the expenditure is x + py. Substitute the values of x(p) from
equation (27) and y(p) from equation (26) into x + py and simplify the resulting expression
as much as you can.
Problem 12 In this example, the firm’s production function is y = f(x) = αxβ. Its profit
function is π(x|p) = p f (x) − x. We determined that the equilibrium price in the example is
p∗ = 29. Graph the profit function and show the maximizing input level for the function and
the profit at when the firm uses its profit maximizing input level. Use the production function
to find the level of output that the firm produces when the firm uses the maximizing input level.
