Final answer:
The slope of the isoquant for the production function at the point (40,80) is calculated by finding the marginal products of x and y and computing the marginal rate of technical substitution, which results in the closest answer being -0.25.
Step-by-step explanation:
The student's question pertains to determining the slope of the isoquant for a given production function at a particular point. The production function given is (x,y) = 60x4/5y1/5. To find the slope of the isoquant at the point (40,80), we must compute the marginal rate of technical substitution (MRTS), which is the negative of the ratio of marginal products of the inputs.
First, we find the marginal products of x and y, denoted as MPx and MPy. The marginal product of x is found by taking the partial derivative of the production function with respect to x, and similarly, the marginal product of y is found by taking the partial derivative with respect to y. Once we have both marginal products, we can calculate the MRTS by dividing MPy by MPx and applying the negative sign, as the MRTS is the slope of the isoquant and represents the rate at which one input can be substituted for another while keeping output constant.
Calculating the marginal products:
MPx = 48x-1/5y1/5
MPy = 12x4/5y-4/5
Then we evaluate these at the point (40,80):
MPx(40,80) = 48(40)-1/5(80)1/5
MPy(40,80) = 12(40)4/5(80)-4/5
Finally, we compute the MRTS:
MRTS = -MPy / MPx = - (12(40)4/5(80)-4/5) / (48(40)-1/5(80)1/5)
After calculating, we find that the closest answer to the calculated MRTS is -0.25, which corresponds to option c.