1. This rst question focuses on nding the short run equilibrium outcome given a par- ticular production function. Assume that a rm is producing using q = IEK1L]={K\"\"'+ L'WJE ie a constant elasticity.r of substitution production function. Suppose the rm cur rently owns 16 machines (i.e. K = 16], the price of the good is P = $3, the rental rate of capital is r 2 Mill, and the wage rate is u: [no number given yet on purpose]. (a) {1 point} What would he the problem the rm is solving here?I (b) {2 points] Using the production function, what is the demand curve for labour? Provide a. rough sketch showing the relationship that would exist in the factor market for labour. (c) {2 points) Suppose the labour supply is perfectly inelastic at L5 I ll) what wage would this suggest? What about if the labour supply was perfectly elastic with w = $10 {nuke sure to nd L]? (d) {4 points} in equilibrium, the market wage is u: 2 $5. What is the optimal level of labour L' and out-put a"! What are prots here? What do the prots suggest the rm should do? {e} [2 points) Find the short run cost mction C(q] for this model; (f) [3 points] What would be the problem the rm is solving if it is using the cost function found in the previous question? Show that q" and prots are the same as during the production approach [i.e. solve the problem to nd if and calculate prots)