Answer to Question #121929 in Microeconomics for Haleema

Question

A firm manufactures quad bikes. Each quad is made using 1 frame (x1) & 4 wheels (x2). Each frame costs 10£ and each wheel costs 4£. The output of the firm can therefore be represented by the function: min [x1, 1/4 x2]
1) what is an isoquant? Show the isoquant for producing 2 quads? 3 quads and 7 quads.
2) define the firms cost function and derive it. Assume that each wheel costs 4£ and each frame costs 10£. What is the cost of producing 7 quads?
3) derive the input demands for frame and wheels for the firm. How do they depend on input prices? What is the maximum number of quads the firm can produce if the number of wheels is fixed at 12? Assume that the firm is producing the maximum number of quads. What is the marginal product of adding an extra frame?

Answer 1

1)

An isoquant, an equal quantity line is a curve demonstrating various variants of combinations of production factors that can be used to produce a given volume of product. Isoquants are otherwise called equal product curves.

The slope of the isoquant expresses the dependence on another factor in the production process. The increase in output.

2)

$$f(x)=10x+4\times4x=26x$$

if x=7, then

$$f(7)=26\times7=182$$

3)

$$f(x)=p_1\times x+p_2\times 4 \times x$$

$$4x=12, x=3$$

If p1=10, p2=4 and x=3

$$f(3)=30+48=78$$