Why does the marginal product of labor decrease with more than four workers in this
example

Define the marginal rate of substitution between two goods (x and y). if a consumer’s preferences are given by u(x,y) = x3/4y1/4, compute the consumer’s marginal rate of substitution as a function of x and y. calculate the mrs if the consumer has chosen to consumer 48 units of x and 16 units of y. show your work. (use the back of the page if necessary.

Experts are particularly concerned about four strategic metal resources that are important for the u.s. economy and military strength, and that must be imported. what percentage does the u.s. import? *

Why is the cournot equilibrium an​ equilibrium? a. there are​ short-run barriers to exit in a cournot​ duopoly, so both firms cannot alter their output levels. b. given the other​ firm's level of​ production, both firms are maximizing profits and cannot improve their situation by unilaterally altering their level of output. c. both firms operate at zero profit under a cournot​ equilibrium, so they would face negative profits if they change output. d. both firms operate at minimum​ long-run average cost under a cournot​ equilibrium, so changes to output would reduce​ long-run profits. even if they​ can't collude, why​ don't firms set their outputs at the joint​ profit-maximizing levels​ (i.e., the levels they would have chosen had they​ colluded)? a. given that other firm produces at the collusive​ level, a firm could increase their own profits by increasing output above the collusive level. b. the midpoint of the collusion curve​ (i.e., the collusive​ outcome) lies below the reaction​ curves, so both firms have an incentive to increase output under the cournot duopoly. c. both a and b are correct d. both a and b are incorrect