Department of EconomicsFall 2002
Principles of Economics
Problem Set #4
1. Define isoquant. What is measured on the axes of a diagram with isoquants? What is the relationship between the isoquant map and the production function?
An isoquant is a curve that shows all combinations of inputs that will produce the same level of output, provided that the inputs are used in a technologically efficient manner (i.e., it is the maximum output you can get for a combination of inputs (L,K)).
The quantities of the two inputs (usually K and L in our examples, but they can be other inputs) are measured on the axes.
The relationship is that an isoquant is a graphical representation of a production function such as Q = f(K,L,F). If we change the production function to be Q = g(K,L,F) then we’d get a different isoquant map.
2. Isoquants are downward-sloping, non-intersecting, convex curves. Explain the basis for each of these characteristics. Isoquants must slope downward so long as each input is productive and has a positive marginal product. Hence, the only way to maintain constant output after increasing the quantity of one input is to decrease the quantity of the other.
Isoquants cannot intersect. If they did, it would mean that the same combination of inputs produces two technically efficient (maximum) levels of output, which is not possible. Isoquants are convex because, as the first input becomes scarcer and the second input more abundant, it becomes more difficult to substitute one input for another and keep output constant. That is, as you downward (to the right) along a convex isoquant, for one-unit increases in Labor, the decline in capital becomes less and less (since labor becomes less and less productive; diminishing MPL). Or similarly, as you move downward (to the right) along a convex isoquant, for one unit decreases in Capital, the...