The isoquant line is described on this forms:
a)y=[x1/2 + x1/2]2 (1/2 should be mark as upper quartile)
b)y=[x12 + x22]1/2 (x1 as lower quartile and 2 upper for first x and same for x22).
The question is how to draw the isoquent line and how to explain the differences between production technology a) and b)
Im having mucho trouble trying to understand your math notation. Understandably, expressing the right mathmatical symbols and notation is quite difficult in Jiskha's pure text posting environment.
Im guessing x1 and x2 are different inputs in the production function. Yes?
A typical production function taught in economics is the so-called Cobb-Douglas, which takes the form A*(K^a)*(L^b), where K is capital, L is labor, A is a constant, and a and b are power terms where a+b=1. Are you starting from a Cobb-Douglas??
Repost. If your original problem has super and subscripts, they will need to be explained.
Sorry I didn´t expl. it correctly and I´m agree it hard without rights symbol. Yes a) x1 and x2 is different input and each have 1/2 square and both in square 2. b) x1 and x2 has square 2 and both in square 1/2. No, it does not start from the cobb-douglas it's only an quastion to draw the line with these two formula (a and b) on the axis to show the isoquant and explain the difference between this two production technology (a and b)
Thank you for providing more clarification. I will proceed with explaining how to draw the isoquant line based on the given formulas (a) and (b), as well as highlighting the differences between the two production technologies.
Isoquant lines represent different combinations of inputs that yield the same level of output in a production process. They depict the various ways inputs can be combined to produce a specific level of output.
Let's start by drawing the isoquant line for production technology (a): y = [x1/2 + x1/2]^2. To generate points on this isoquant line, we need to select different combinations of x1 and x2 that satisfy the equation.
One approach is to select different values of x1 and calculate corresponding values of x2 using the given equation. For instance, if we choose x1 = 1, then x2 can be calculated as follows:
y = [1/2 + 1/2]^2 = [1]^2 = 1
Thus, the point (1, x2) lies on the isoquant line. By repeating this process for various values of x1, we can obtain multiple points, and connecting them will give us the isoquant line for production technology (a).
Now, let's move on to drawing the isoquant line for production technology (b): y = [x1^2 + x2^2]^(1/2). Similarly, we need to find different combinations of x1 and x2 that satisfy this equation.
Using the same approach as before, we can select different values of x1 and calculate corresponding values of x2. For instance, if we choose x1 = 1, then x2 can be calculated as follows:
y = [1^2 + x2^2]^(1/2) = 1
By solving this equation for x2, we find that x2 = 0. Thus, the point (1, 0) lies on the isoquant line. Repeating this process for other values of x1 gives us multiple points, and connecting them will yield the isoquant line for production technology (b).
Now, let's discuss the differences between the two production technologies based on their respective isoquant lines:
1. Shape: The isoquant line for production technology (a) is concave upward, meaning it curves upwards as we move away from the origin. On the other hand, the isoquant line for production technology (b) is a circle or spherical shape centered at the origin.
2. Elasticity of Substitution: The isoquant line for production technology (a) exhibits a decreasing marginal rate of technical substitution. This implies that as one input is substituted for another while keeping the level of output constant, the rate at which the inputs can be substituted decreases. In contrast, the isoquant line for production technology (b) exhibits a constant marginal rate of technical substitution, meaning inputs can be substituted at a constant rate without affecting the level of output.
3. Complementary and Substitutable Inputs: The isoquant line for production technology (a) suggests that inputs x1 and x2 are complements, as they are combined in equal proportions. In contrast, the isoquant line for production technology (b) implies that inputs x1 and x2 are substitutes, as they can be substituted at a constant rate while maintaining the same output level.
By analyzing these differences, we can gather insights into the nature of the production technologies and how inputs are combined to achieve a specific level of output.