4. To produce traps the coyotes requires capital K and labour L. Neither by itself produces good traps. Suppose that the production technology can be captured by the production function q=201°5Kos where q is number of traps, MPL =10L-05Ks, and 0.5 0.5 a) What can you say about the returns to scale for this production function? b) What is the equation of isoquant? c) What is the equation for a slope of an isoquant? What is this called? What does it indicate? d) Set up the cost minimization problem and solve for the conditional capital and labour demands as functions of w (the labour costs) (the capital costs), and q (number of traps) e) What is the equation of the expansion path? Discuss your findings. f) Discuss the demand functions you derived in d). Are production inputs the normal inputs? What happens to optimal amount labour as w increases? What happens to optimal amount of capital as r decreases? g) Now, assume that the cost of the labour is S10 while cost of capital is $40. What is your "optimal production plan"? h) Derive the cost function and simplify the function as much as you can. i) What is your "optimal production plan" if you wish to produce 100 traps? j) What is the cost of producing 100 traps?
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