Cumberland’s Contracting uses linoleum, l, and vinyl, v, panels to produce floors in homes.
The two inputs are perfect substitutes, but due to the slightly higher quality of their vinyl supplier,
the marginal product of vinyl panels is three floors and the marginal product of linoleum panels is two
floors. These marginal products are constant.
(a) (3) Write down the production function relating output to the amount of linoleum and vinyl
panels used in production (f(ql,qv)).
(b) (3) Given your production function in part (a), does the firm’s technology exhibit increasing,
constant, or decreasing returns to scale? Justify your answer.
(c) (6) Graph the isoquants corresponding to 6, 12, and 24 floors produced with linoleum panels on
the horizontal axis and vinyl panels on the vertical axis. Label all relevant slopes and intercepts,
as well as each isoquant. What is the MRTS?
(d) (8) Suppose that each package of linoleum paneling costs $50 and each package of vinyl paneling
costs $100. Derive an expression for a firm’s minimum costs of producing f floors, taking into
account the input bundle the firm demands and showing clearly how you arrived at your answer.