Question

6. What do we mean by an isoquant? Why is it downward sloping? Why is it convex?

(a) Find the equation for an isoquant with Q= 48 for the production function Q= 24 L^1/4 K^1/4 :

Prove that it is downward sloping and convex.

(b) What kind of returns to scale does the production function given above exhibit? What do we mean by that? What would the long-run average total cost look like?

(c) Suppose price of labor

(w) = 1 and price of capital (r) = 2. The market price for the output produced is P= 12.

For the production fumction given above,

i. find out the short-run cost function C (Q) I_k=81 , and

ii. the profit maximizing choice of output and labor in the short-run. How much is the profit?

Answer 1

Isoquant is a curve showing different combinations of inputs to produce a constant level of output. It is downward sloping generally, as it depicts how in order to increase the use of one input, another input has to be sacrificed. The slope is called the marginal rate of technical substitution. It is convex implies that one has diminishing MRTS as one moves along the isoquant curve substituting one input for the other and the opportunity cost declines as the rate of substitution increases.