Slope of the firm isoquant

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1. A firm has the production function, f(x, y) = 20x3/5y2/5. The slope of the firm's isoquant at the point (x; y) = (80; 10) is: (Pick the closest one.) answer is -0.19, please show steps and explain, thank you.

2. A firm has the production function f(X, Y ) = X3/4Y1/4 where X is the amount of factor x used and Y is the amount of factor y used. On a diagram we put X on the horizontal axis and Y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of -3. The straight line we drew: (ans is C, please show steps and explain.)

(a) is vertical.

(b) is horizontal.

(c) is a ray through the origin with slope 1.

(d) is a ray through the origin with slope 2.

(e) has a negative slope.

3. A firm has the production function f(x1,x2)=x10.40x20.20 . The isoquant on which output is 402/10 has the equation? the ans is x2 = 40x1-0.20 please show steps and explain. 

4. A firm has a production function f(x, y) = 1(x0.80+y0.80)4 whenever x > 0 and y >0. When the amounts of both inputs are positive, this firm has: increasing returns to scale. Please explain.

Reference no: EM131423698

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