Answer to Question #202371 in Microeconomics for Ondisa

Question

Given the production function:

 Y = 10 + 5X₁ – 0.2 X₁²

a)  Define the functions for average product and marginal product.

b)  Compute the maximum level of production of Y and the corresponding    level of input X_1.

c)        Given the price of Y = R3.75/unit and that of X₁ = R1.50/unit, algebraically compute the maximum profit level of input and output.      

Answer 1

a)

$$AY=\frac{10}{X_1}+5-0.2X_1$$

$$MY=5-0.4X_1$$

b)

$$5-0.4X_1=0$$

$$X_1=12.5$$

$$Y=41.25$$

c)

$$\pi=41.25\times3.75-12.5\times1.5=135.94$$