Suppose Ralph hires workers at his supermarket at a wage rate of $12/hour. Ralph currently has 10 checkout stands (i.e., capital), each with a rental rate of $10/hour. The production of customers served (i.e., output) is determined by the hourly production function: Q = 0.5L0.75K2. For the questions that follow, the number of checkout stands is fixed. Show your work clearly.
(a) Graph Ralph’s TP curve.
(b) On a new graph, graph Ralph’s MPL and APL curves.
(c) Derive Ralph's short-run total cost function.
(d) Derive the corresponding equations for the marginal cost (MC), average variable cost (AVC), average fixed cost (AFC), and average total cost (ATC) functions.